## Simpson S Rule Questions and Answers

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Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. \int_0^2 {5x{e^{ -...

Use 4 sub-intervals to approximate integral_{0}^{{2 pi} / 3} cos (x) dx and calculate as good a bound as possible on the error using Simpson's Rule. Give your answer as a decimal accurate to at lea...

Use the Simpson's Rule to approximate the following integral with the specified value of ''n'': \int_{0}^{4} e^{4 \sqrt{t}} sin(4t) \: dt, \; n =8.

Approximate the following integral using Simpson's Rule: \int_{0}^{3x/5} 5 \: sin(10x) \: cos(5x) \: dx = \dfrac{4}{3}. Experiment with values of ''n'' to ensure that the error is less than \rm 10^...

Approximate the following integral using Simpson's Rule. Experiment with values of n to ensure that the error is less than 10^{-3}. integral_0^{pi / 3} 3 sin (18 x) cos (9 x) dx = 4 / 9

Evaluate the following integral using the Simpson's rule with 6 equally segments: \int_{0}^{6} \sqrt{4+x^2} \: dx.

Use the error formula to find n such that the error in the approximation of the definite integral is less than or equal to 0.0002 using Simpson's Rule. integral_0^{pi/4} cos (x^2)dx

Use the Simpson's rule with n=6 to approximate the area under the right half of the Gaussian distribution function corresponding to mean 0 and standard deviation 1, i.e., approximate integral from...

Use Simpson's Rule with n = 8 to estimate the length of the curve y = x^2 e^x on x more than or equal to 0 and less than or equal to 2.

Estimate the numerical value of\int^{\infty}_{0} e^{-x^2} dx by writing \int^{\infty}_{0} e^{-x^2} dx =\int^{4}_{0} e^{-x^2} dx + \int^{\infty}_{4} e^{-x^2} dx

Consider the following \int_{0}^{1/2}10 \sin(e^{7t/2})\,dt ; n=8 (a) Use the Trapezoidal Rule to approximate the given integral with the specified value of n. (b) Use Simpson's Rule to approxi...

The following table gives the approximate amount of emissions E of nitrogen oxides in millions of metric tons per year in the US. Let t be the number of years since 1940 and E = f(t). Estimate the...

Given the integral integral_1^2 1/x dx a. Evaluate the exact value of the integral. b. The Simpson's Rule. i. Estimate the integral using the Simpson's rule with n=4.(5 D.P.) ii. Find an upper boun...

Consider \int^5_1 ln x dx. Use If |E_s|\leq \frac{K(b-a)^5}{180n^4}.

Find an n such that Simpson's S n is within 10 8 of 3 0 1 ( x + 2 ) d x . The error bound for Simpson's rule on int b a f ( x ) d x is M 4 ( b -a ) 5 / 180 n 4 , where M 4 is any...

Use the Simpson's Rule to approximate the given interval with the specified value of ''n'': \int_{1}^{2} \sqrt{x^3 -1} \: dx, \; n = 10.

Use simpson's rule to calculate \int_{2}^{5}\frac{1}{x+1}dx with n=10 steps.....estimate \left | E_{5} \right |

Approximate the integral \int^5_1 \frac{\cos x}{x} dx using M_8 and S_8. a. Find an upper bound for the error in using M_8 as an approximation. b. Find an upper bound for the error in using S_8 as...

Estimate the minimum number of subintervals needed to approximate the integral \int^4_2 \frac {1}{x -1} dx with an error of magnitude less than 10^{-4} using Simpson's Rule.

Find an upper bound for the error in estimating integral \int_{-1}^4(3x^2+8x)dx. Please show all steps.

Find n such that the error in approximating the given definite integral \int\limits_0^5 x^4 \text{d}x is less than 0.0001 when using: a) the Trapezoidal Rule, b) the Simpson s...

Recall from class the curve given by the intersection of the cylinder x^2 + y^2 = 2 and the plane x + z = 4. Use Simpson's Rule with n = 8 intervals to approximate the arc length of the curve r(t)...

Write an integral that represents the length of the curve y = sin(x) for 0 \leq x \leq \pi. Use Simpson's rule with n = 4 to approximate the value of the integral, correcto to within \pm 0.001

a. Find the approximations T_10 , M_10 , S_10 for int_0^pi 11sin x dx. Find the corresponding errors E_T, E_M, E_S. b. Compare the actual errors in part (a) with the error estimates given by t...

How large must n be to guarantee that the Simpson's rule approximation for integral from t=0 to pi/2 of sin(3t+1) dt is accurate to within 10^(-5)?

1) Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) integral dx / 22 + 5 e^x - 15 e^{-x}. 2) The region bounded by the curve y = 2...

The integral I = integral^pi_0 e^x cos (x) dx is approximated by the Trapezoid and Simpson's rules at equally spaced points. How many such points are needed by Trapezoid and Simpson's rules, respec...

Use Simpson's Rule to approximate the average value of the temperature function f(x) = 37\sin (2\pi /365(x - 101)) + 25 for a 365-day year. This is one way to estimate the annual mean air temperatu...

Approximate the integral \int_{1}^{5}\sqrt{3+x^{2}}dx with n=4 using the specified method

Water leaks from a tank at a rate r ( t ) gallons per hour. Estimate the total amount of water that leaks out during the first four hours, using... t 0 0.5 1 1.5 2 2.5 3 3.5 4 r(t) 4.00 2.82 2.1...

The table below gives the power consumption in megawatts in Hartford County from midnight to 3:00 A.M. on a day in December. Use Simpson's Rule to estimate the energy used during that time period....

Calculate the S_6 approximation for the following integral. Please write the formula and y values being used for approximation in your work. Then find the true value and calculate the error in you...

Find the approximations T_{10}, M_{10}, and S_{10} for \int_3^8 \sin x \, dx

Approximate \int_0^3 \dfrac{dx}{1 + x} using Simpson's rule, where n = 6 to 4 decimal places.

Approximate to 4 decimal places using Simpson's Rule and n-6. \int_{0}^{\pi}3ln(\sin x+1)dx

Consider the following integral: I = \int^{\frac{3}{2}}_1 x \ln(1+x)dx. (1) Use the Mid point rule to estimate the value of I with a maximal absolute error of 0.0001 (round your answer to three dec...

How would you compare the relative merits of Simpson's Rule and the Trapezoidal Rule?

We often need to use numerical integration when we cannot apply the Fundamental Theorem of Calculus. Let us investigate \int_{0}^{2}\sqrt{1 + 9x^4}dx, an integral that we cannot do exactly in the c...

Use Simpsons's rule to estimate the following integrals, where E_S is the error bound. A) \int_0^1 e^{\sin x} dx, |E_S| less than 0.001 B) \int_0^1 \sin (x^3) dx, |E_S| less than 0.02

Use Simpson's Rule with n = 100 to evaluate the integral \int_0^3 ( 3 \sqrt{t e^{-4.2t}} i + 4e^{-0.8t^2} j) \, dt

4. The table below gives power consumption p in megawatts in Luxembourg t hours after midnight on a day in December.

For any pre-determined error bound, can you find an approximation with error smaller than that bound?

Approximate the values of the integrals of the function defined by the given set of points by using simpsons rule. \int_{2}^{14}y dx x: 2, 4, 6 ,8, 10, 12, 14 y: 0.67, 2.34, 4.56, 3.67, 3.56, 4.7...

Here are four ways to compute Definite Integrals. Show two or three more ways like these to compute definite integrals. integral_{x_0}^{x_n} f(x) dx approx h Sigma_{i=0}^{n-1} f(x_i) integral_{x_0}...

Estimate the numerical value of e-x2 dx by writing e-x2 dx = 04 e -x2 dx _ 4 e-x2 dx a) Approximate the first integral using Simpson's Rule with n = 8 subintervals. b) Compute the following integra...

Suppose you are asked to estimate the volume of a football. You measure and find that a football is 28 cm long. You use a piece of string and measure the circumference at its widest point to be 53...

Use Simpson's Rule with n = 10 to approximate the length of the arc of r(t) = ti + t^2j + t^3k from the origin to the point (2, 4, 8).

Construct a definite integral that calculates the length of the arc y = \sin x, \ \ 0 \leq x \leq \pi. Then use the Simpson's method with n = 6 to find an approximation of the length of the arc. Us...

The graph of y = f(x) is shown over ~[0.4] along with a table of numerical data. Use this data and Simpson's Rule with n = 4 subintervals to estimate the volume of the solid obtained when the regio...

Which formula, Trapezoidal or Simpson s, gives the better approximation when using the same number of terms in the expansion? Why?

Use the Simpson's Rule to approximate the following interval using n = 6: \int_{0}^{3} \dfrac{1}{8 + y^5} dy.

Use Simpson's rule with n= 10 to approximate \ln(2) = \int_1^\# \frac{dx}{x}.

It has been estimated that service industries, which currently make up 30% of the non-farm workforce in a certain country, will continue to grow at the rate of R(t)=8e^(1/(4t+7)) percent per decade...

It has been estimated that service industries, which currently make up 30% of the nonfarm workforce in a certain country, will continue to grow at the rate of R(t)= 6e^(1/(2t+1)) percent per decade...

An oil rig is leaking into the water, with the rate of leakage estimated as follows: \begin{array}{|l|l|l|l|l|l|l|l|} \hline day & 0 & 15 & 30 & 45 & 60 & 75 & 90\\ \hline rate (10^3 barrel/day) & 62

Set up an integer representing the is the length of the curve y=2(1+x^{2})^{\frac{1}{2}} from (0,2) to (1,2\sqrt{2}) and use Simpson's parabolic rule n=2 (that is, with two subintervals) to estimate

Use Euler's method to make a table for the approximate solution of the differential equation d y d x = 1 + 3 x - 2 y , with initial condition ( 1 , 2 ) using 2 step sizes, h = 0.2 and h = 0.1 ,

Use trapezoidal rule to solve
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\displaystyle \int_{a}^{b} (Ax^2 + Bx + C)dx = \frac{(b-a)}{6} \left[P(a) + 4P\left(\frac{a+b}{2}\right) + P(b)\right]}]
[{MathJax fullWid...

Calculate the integral approximations T 6 | and M 6 | for ? ? 3 0 s e c 2 x d x

Use the Simpson's Rule with n=6 to estimate the volume of the curve rotated about the x-axis y=sin(\frac {1}{x}) 1 \leq x \leq 4

Consider the region bounded by y = \sqrt{\tan x}, y = x, and x = \frac{\pi}{4}. Find the area of this region using S_6. Further, suppose that the upper bound for the fourth derivative of the requir...

How large should n be to guarantee that the Simpson's rule approximation to integral^1_0 e^{x^2} dx is accurate to within 0.00001?

Use S4 to estimate taking the value of at x = 0 to be 1. (Round your answer to three decimal places.)

Use the following table to estimate the value of the integral from 4 to 19 f(x)dx using Simpson s rule.

The length of the ellipse x = a cos t, y = b sin t, 0 less than equal to t less than equal to 2 pi is L = 4a integral_0^pi/2 squareroot 1 - e^2 cos^2 t dt, where e is the ellipse's eccentricity. Us...

Given the following integral \int^1_0 \frac {16 (x - 1)}{x^4 - 2x^3 + 4x - 4}dx a. Evaluate the above integral. b. Let the step side to be 0.1, apply the Simpson's rule to obtain a numerical sol...

The velocity v ( t ) ft/sec of an object moving on the x -axis at t sec is recorded as t 2.0 2.25 2.50 2.75 3.0 3.25 3.5 3.75 4.0 v(t) 5.21 6.14 7.24 6.79 6.15 5.89 5.96 6.18 9.89 Using Simps...

f(1)= 20, f(3)=13, f(5)=15, f(7)=16, f(9)=11, on ~0,6 a. used midpint rule with n=5 to estimate { \int_0^{10} f(x)dx } b, use trapezoidal rule with n=4 to estimate { \int_0^9 f(x)dx } c, used...

Find the integral integral 10 0 6 x 3 - 18 x - 32 x + 5 x 3 - 3 x - 10

Antiderivative of ((\frac {(x^3)}{6}) + \frac {1}{2x})^*\sqrt{(\frac {1}{2} + (\frac {(x^4)}{4}) - (\frac {1}{4x^4})})

The design of a new airplane requires a gasoline tank of constant cross-section in each wing. The tank must hold 5000 lb. of gasoline that weighs 42 lb/ft^3. a. A scale drawing of a cross-section...

The accompanying table gives data for the velocity of a vintage sports car accelerating from 0 to 142 mi/hr in 36 sec (10 thousandths of an hour) | 0.0 | 0 | 0.001 | 49 | 0.002 | 62 | 0.003 | 82 |...

When is right endpoint approximation more accurate than Simpson's rule?

Use Simpson's rule to approximate the integral with n = 4. integral_0^{pi} sin (x) dx. Calculate the bound for the error in your answer.

Estimate the given integral as defined by the provided data

A vertical, irregularly shaped plate is submerged in water. The table shows measurements of its width, taken at the indicated depths. Use Simpson's Rule to estimate the force of the water against t...

Approximate the value of the integral defined by the given set of points. \int_{0}^{12} y \space dx (Give your answer to 2 decimal places.) HtmlTable <table><tr><th>x</th><th>0</th><th>2</th><th>4...

{ f(x) = \sqrt{\frac{5}{x}} + 2 } use sympson's rule with N=6 to evaluate the integral of the following function over x& ~1,2

Approximate the integral \int_{-1}^{0} e^{x^2} dx Using Simpson's Approximation based on 4 sub intervals. Clearly state which definition of Simpson's Approximation you are using.

Approximate the following integral using the methods indicated with n = 4 subdivision. integral from 0 to 1 of e^{-2x^2} dx

Use the simpson's rule with n=10 to estimate arc length of y=x^{-1/3}, for 1 \leq x <6.

Using Simpson's Rule, calculate the integral integral^5_1 ({x^3}/{4} + x + 2) dx for n = 2.

1.) How large should n be to guarantee that the Simpson's Rule approximation to \int_{1}^{2}\thinspace e^{1/x} is accurate to with 0.00001? 2.) Evaluate the integral \int_{0}^{1}\frac{2x+3}{(x+1)^2...

Use the error bound to find the smallest value of N for which Error(S_N) less than or equal to 10^{-9}. integral_0^1 11 e^{x^2} dx.

Use the error bound to find the smallest value of N for which Error(S_N) less than or equal to 10^{-9} . \int_{1}^{3} x^{\frac{4}{3}} dx

Use the error bound to find the smallest value of N for which Error(S_N) \leq 10^{-9}. \int_{1}^{5} x^{\frac{4}{3}} dx N= \; \rule{20mm}{.5pt}

Use the error bound to find the smallest value of N for which Error(S_N) \leq 10^{-9}. \displaystyle \int \limits_{1}^{3} x^{4/3} \ dx

The table (supplied by San Diego Gas and Electric) gives the power consumption P in megawatts in San Diego County from midnight to 6:00 am on a day in December. Use Simpson's Rule to estimate the e...

Find the smallest n such that the error estimate in the approximation of the definite integral is less than 0.00001 using Simpson's Rule.

Find n such that the error in approximating the given definite integral \int\limits_1^4 \frac{1}{\sqrt{x}} \text{d}x is less than 0.0001 when using: a) the Trapezoidal Rule, b)...

Use the error formula to find the smallest n such that the error int he approximation of the definite integral is less than 0.00001 using the following rules: a. The Trapezoidal Rule, b. Simpson's...

Use Simpson's Rule to approximate the integral. Show values of h, yo, y1, etc. \int_2^4 dx/(x^2 + 1); n=8

Use the table below and Simpson's Rule with n = 10 subintervals to approximate the integral of f(x) over x from 0 to 2. x = {0, 0.2, 0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6, 1.8, 2}, f(x) = {4.8, 5.5, 4.7,...

Consider the ='false' \int^3 _{-3} x^{-2} e^x dx. Using 6 sub intervals estimate the integral with Simpsons Rule.

Estimate the error if S_7 (Simpson's rule with n = 7) was used to calculate integral_0^3 sin(2 x) dx .

Solve (a) Use Simpson's Rule, with n=6, to approximate the integral \int 7e^{-4x}dx. (b) The actual value of \int 107e^{-4x}dx. (c) The error involved in the approximation of part (a) is E_S=\int...

How large do we have to choose n so that the approximations T_n, M_n and S_n to the integral \int_{1}^{2}\frac{1}{x}dx are accurate to within 10^{-4}?

Use Simpson's Rule with n = 4 to estimate the arc length of the curve y = 1.5e^{-2x}, 0 \leq x \leq 2.

Use the midpoint rule and Simpsons' rule to approximate the following integrals with the specified value of n. Round your answers to the nearest six decimal places. Compare your answers to the actu...

Find an upper bound for the error in estimating \int_0^\pi {2x\cos \left( x \right)dx} using Simpson's rule with four steps.

Estimate the area under the curve in the interval [0, 3] with n = 6 using Simpson s Rule.

Estimate the area under the curve f(x)=\sqrt{x-5} in the interval (0, 3) with n = 6 using Simpson's Rule.

Find the approximations T_n, M_n and S_n for n = 6 and 12. Then compute the corresponding actual errors E_T, E_M and E_S. (Round your answers to six decimal places. You may wish to use the sum comm...

Calculate the maximum possible error associated with each estimate below. int_0^1 sin(x^2)/1+xdx. The two graphs show the second and fourth derivatives of sin(x^2)/1+x on the interval [0,1]. a....

Find an upper bound for the error in estimating \int_{2}^{6} \frac{1}{x-1} dx using Simpson's Rule with n = 8 steps.

Approximate the area under the curve defined by the following data points. x 1 4 7 10 13 16 19 22 25 y 2 4.6 7 6.2 6 5.5 4 7.8 8

Calculate S_N given by Simpson's Rule for the value of N indicated. (Round your answer to three decimal places.) \int_2^5 \sqrt{x^4 + 5} dx, N = 4

Use the error formulas to find the smallest n such that when \int_{0}^{20}sin(3x)dx is approximated using the trapezoidal rule and Simpson's rule, the error is less than 10^{-4}.

\int^2_0 (\frac {cos (x)}{2}- 4x^2 + 17) Evaluate the integral with simpson's rule with n =6.

Use Simpson's Rule with n = 10 to approximate \int_1^2 \dfrac{1}{x}\ dx.

With n = 10, approximate the integral \int_0^{\frac{\pi}{2}} \sin x dx using Simpson's rule and the trapezoidal method.

Find n so that S_n (Simpson's rule with n subintervals) is guaranteed to approximate \int _ { 0 } ^ { 5 } \operatorname { sin } ( 3 x ) d x to within 0.001.

Find n, so that S_n (Simpson's rule with n subintervals) is guaranteed to approximate ?_0^3 sin(3x) dx to within 0.002.

Find n so that S_n (Simpson's rule with n subintervals) is guaranteed to approximate \int _ { 0 } ^ { 3 } \operatorname { sin } ( 3 x ) d x to within 0.002

Find n so that S_n| (Simpson's rule with n subintervals) is guaranteed to approximate \int_0^3 \sin(3x) dx| to within 0.002. a) n \geq 24| b) n \geq 16| c) n \geq 7| d) n \geq 8| e...

Use Simpsons rule to approximate the integral \int_{-3}^1 x \cos(\frac{19x}{2}) \, dx

Use Simpson's rule to approximate the integral int_-3 ^1xcos(19x 2 ) dx.

Estimate using Simpson's rule with n = 6 subintervals for \int_{-3}^{4} f(x) dx.

Using Simpson's Rule with n = 6, calculate the value of the integral. integral_{-2}^2 (x^2 - 2) dx.

Use Simpson's Rule and n = 6 to approximate the integral int_{2}^{8} (1/2)^x d x.

Use Simpson's rule to calculate the following definite integrals: displaystyle I_1 = 3600 cdot int^{12}_0(12t^2 - t^3)cdot dt and displaystyle I_2 = int^6_1 dfrac{2}{(3x - 2)^{3/4}} cdot dx

Use the Trapezoidal and Simpson's rules to calculate the following definite integral. I = 3600 \cdot \int\limits_0^{12} {\left( {12{t^2} - {t^3}} \right)} dt

How large do we have to choose n so that the approximation in Simpson's rule to the integral from 0 to 1 of (e^x + 4x^5)dx is accurate up to 0.00001?

Find the smallest number of partitions so that the approximation to f(x) = 4 ln x from integral a = 1 and b = 7 using Simpson's Rule is accurate to within 0.0001.

The following table gives the power consumption in megawatts for a region from midnight to 6:00 AM on a particular day. Use Simpson's Rule to estimate the energy used during this time period. (Roun...

The following table gives the power consumption in megawatts for a region from midnight to 6:00 AM on a particular day. Use Simpson's Rule to estimate the energy used during this time period. t&P...

Construct a definite integral that calculates the length of the arc y = sinx, 0 less than or equal to x less than or equal to pi. Then use the Simpson's method with n = 6 to find an approximation...

How large should n be to guarantee that the Simpson's rule approximation to \int_{0}^{1}13ex^{2}dx is accurate to within 0.00001?

How large should n to be to guarantee that the Simpson's Rule approximation to \int_{0}^{1} 11e^{x2}dx is accurate to within 0.0001?

How large should n be to guarantee that the Simpson's Rule approximation to int_{0}^{1} 3e^{x^2} is accurate to within 0.00001?

Use the Simpson's Rule, to find the given integral with the specified value of n. int_{1}^{5} 2 cos (2x)/x dx, n=8.

Use Simpson's Rule with n = 10 to approximate 2 1 1 x d x

Estimate the minimum number of sub intervals to approximate the value of \int_{-3}^3 (4x^2+7) \,dx with an error of magnitude less than 5 \times 10^{-4} using a. the error estimate formula f...

Use the Simpson's Rule and approximate integral_0^2 x square root {x^2 + 1} dx up to 3 digits after the decimal point (rounded), for n = 4.

Use Simpson's rule with n = 10 to approximate integral^2_1 {cos(x)} / x dx.

Use the error bound to find the smallest value of N for which Error(SN) is less than or equal to 10^9.

Use the Simpson's rule to approximate the given integral with the specified value of n. int_{0}^{4} 5 cot (square root{2x}) dx, n=10

Use the trapezoid rule and Simpson's rule to approximate the value of \int_{0}^{8} x \sqrt{x^2 + 7} \; \mathrm{d}x with n = 4. Then find the exact value of the integral.

Estimate the integral \displaystyle \int_0^2 \frac{1}{\sqrt{x^3 + 2}} dx by Simpson's rule using n = 8.

Use Simpson's Rule to approximate the integral \int_{0}^{1/2} \sin(e^{t/2})\,dt with the n = 8 .

Use Simpson's rule with n = 6 to approximate ? 1 0 e ? x 2 d x Determine the length of the curve for y = l n ( s i n x ) for ? 4 ? x ? ? 2

Use the Simpson's Rule to approximate the given integral with the specified value of ''n'': \int_{1}^{5} \dfrac{6 \: cos(4x)}{x} dx, \; n = 8.

Use the Simpson's Rule to approximate the given interval with the specified value of ''n'': \int_{1}^{3} e^{1/x} \: dx, \; n = 8.

Use the Simpson's Rule to approximate the given interval with the specified value of ''n'': \int_{0}^{4} x^3sin(x) \: dx, \; n = 8.

Estimate \int^\pi_0 f(x) dx as accurately as possible, where f(x) is defined by the data \begin{array}{|c|c|c|c|c|c|} \hline x& 0 & \frac{\pi}{4} & \frac{\pi}{2} & \frac{3\pi}{4} & \pi \\ \hline f(...

Using Simpson's Rule: Estimate the integral int_0^pi (4sin(x)dx with n = 4 steps and find an upper bound |E_S|. |E_S| less than or equal to _____ Now evaluate the integral directly and calculate...

1) Use the Midpoint Rule to approximate ? 4 1 e ? x d x f o r n = 4 2) Use the Trapezoid Rule to approximate ? 4 1 e ? x d x f o r n = 4 . 3) Use Simpson's Rule to approximate ? 4 1 e...

1. (a) Use Simpson's Rule with n =4 to approximate the value of \int^3_1 x \ ln \ x \ dx. (Set your calculator to display four places to the right of the decimal.) (b) Use the error estimate...

Find n such that the error in approximating the given definite integral \int\limits_0^\pi \sin x \text{d} x is less than 0.0001 when using: a) the Trapezoidal Rule, b) the Si...

Approximate the following integral: \int \limits_0^1 \arctan (x) dx, \ S_{12}. Additionally, determine the error.

\int_0^4 e^{2 \sqrt t} \sin (5t) dt using trapezoidal rule, midpoint rule, and Simpson's rule. n = 8, round to 6 decimal places.

Suppose you have to approximate \int_2^4 \frac{1}{x}dz to within 0.001. Using Simpson's rule, how large should n be to satisfy the requirement?

Use calculator and Simpson's rule to integrate. Round to four decimal places. \\ \int_0^3 2x^3 dx, \ n=6

Estimate the minimum number of subintervals to approximate the value of \int_0^9 \sqrt{7x+6}dx with an error of magnitude less than 5 \times 10^{-4} using a. the error estimate formula for the Tra...

Given the following definite integral and n = 4 . Answer the following questions. 1.5 0 sin ( x 2 ) d x 1. Use the Trapezoidal Rule to approximate the definite integral. 2. Use the Midpoint Rul...

Calculate the integral \int_0^6 (x^4 - x^2 + 1) dx by using the Simpson's method and estimate the error for n=6.

Use the Simpson's Rule to approximate the given integral using 4 equal subintervals: \int_{1}^{2} \dfrac{ln(x)}{5+x} dx.

Integrate the following function both analytically and using Simpson's method with n=4 and 5. \int_{-3}^{5}(4x-3)^3dx

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis to six decimal places. y = ln(x) 4 greater than or equal to x less than or e...

Approximate the error associated with the Simpson's rule estimate of this integral: \int _{-1}^1 e^{-t^2} dt

1. Using [{MathJax fullWidth='false'
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(a) Trapez...

int_{1}^{4} frac{1}{sqrt{x}}dx Find n such that the error in approximating the given definite integral is less than 0.0001 when using: (a) the Trapezoidal Rule (b) Simpson's Rule

Using the integral from 0 to 1 1/x+1 dx, n = 6, How many subintervals would be needed for Simpson's approximation for the error to be less than 0.00001?

Use the Simpson's Rule, to find the given integral with the specified value of n. int_{1}^{4} 9 square root{ln x} dx, n=6

Approximate to five decimal places the area under the curve y=sin x over the interval [0, pi] using Simpson's Rule with n=4.

Use Simpson's Rule to obtain your best approximation to the following integrals: I_3 = \int_0^{\pi/2} \cos ^7 x \ dx I_4 = \int_0^1 x^2 \ln^3 x \ dx

Apply Simpson's Rule to approximate the value of the definite integral using 4 subintervals: \int^4_1 \sqrt {1+x^2} dx

(a) Evaluate int 1 2 dx / x2 by using Simpson's Rule with n = 4. (b) Find a bound on the error in approximating the definite integral using Simpson's Rule.

Calculate S_N given by Simpson's rule for the value if N indicated (round to five decimal places) integral_0^3 dx / {x^3 + 7}, N = 6.

Calculate S_N given by Simpson's Rule for the value of N indicated. (Round your answer to six decimal places.) integral_{1}^{2} e^ {-4 x} dx, N = 6.

How to estimate area under a curve using left and right Riemann sums with a small number of rectangles? What are other possible ways to improve the estimate? List up to 5 ways to (potentially) and...

Use Simpson's Rule and all the data in the following table to estimate the value of the integral \int_{27}^{33} ydr x = 27, x = 28, x = 29, x = 30, x = 31, x = 32, x = 33 y = -9, y = -2, y = 4...

Use Simpson's Rule with n = 4 to estimate the arc length of the curve, L. Give the answer to six decimal places. y = sec(x), 0 less than or equal to x less than or equal to pi / 6.

Evaluate: Using Simpson's Rule with n=6, calculate the value of the integral \int_0^6 (x^{2-3x} dx

Use Symposia's rule with n=6 to estimate the length of the curve [{MathJax fullWidth='false' y = \sin x; 0 \leq x \leq \pi }]

Consider a function g satisfying the following: |x|g(x) |1.0|3.167 |1.2|3.248 |1.4|3.421 |1.6|3.972 |1.8|3.815 |2.0|3.532 |2.2|3.326 To the nearest .001, approximate \int_{1.0}^{2.2} g(x) dx using

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. y = tan x, 0 less than x less than pi / 9.

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. x = y + y^{1/2}, 1 less than or equal to y le...

Use Simpson's Rule with n= 10 to estimate the arc length of the curve y = \ln(7 + x^3), 0 less than or equal to x less than or equal to 5. Compare your answer with the value of the integral produce...

Use the inequalities |E_M|= |integral_a^b f(x) dx - M_n| less than or equal to (b-a)^3 K_2 / 24n^2 |E_T|= |integral_a^b f(x) dx - T_n| less than or equal to (b-a)^3 K_2 / 12n^2 |E_S|= |integra...

Use Simpson's rule with n=8 to calculate I = \int_0^\pi e^x \cos(x) \, dx

Evaluate the following integrals: (a) \int^1_0 (\frac {2x + 3}{x^3 + 3x + 1}) dx (b) \int^5_0 (\frac {x}{\sqrt {x + 4}}) dx

Apply Simpson's rule to the integral: \displaystyle \int_0^8(6x^5-4x^3)\ dx=258,048.

Use Simpson's to approximate the given integral with the specified value of n. int_{1}^{5} 2 cos(2x)/x dx, n=8.

Find the integral of e^{-x} dx from x = 0 to 1 with Simpson's rule using 10 strips.

A function f is given by the following table: Approximate the area between the x-axis and y = f (x) from x = 0 to x = 4 using Simpson's Rule.

Find the samllest values of n which will guarantee an error less than 0.001 for the \int_0^{\pi} \cos x using both trapezoid and simpson's rules.

Find the approximations T_n, M_n, and S_n for n = 6 and 12. Then compute the corresponding errors E_T, E_M, and E_S. (Round your answers to six decimal places.) Integral from 0 to 2 of 33x^4 dx. Wh...

Given Integral from 2 to 4 of square root of (1 + sin (x^3) times dx, find the approximations T_n, M_n and S_n for n = 6. Then compute the corresponding actual errors E_T, E_M and E_S. Round your a...

Find the approximation S_n to the integral integral_{-1}^2 x e^x dx for n = 6 and then compute the corresponding error E_s.

Use the Simpson's rule with n = 4 to evaluate: \int_0^{2} \sqrt{1 + x^3}dx.

Estimate the area under the curve f(x)=?x+1 in the interval [0, 4] with n = 8 using Simpson

Estimate the area under the curve f (x) = square root x + 1 in the interval [0, 4] with n = 8 using Simpson's Rule.

The widths (in meters) of a kidney-shaped swimming pool were measured at 4-meter intervals as indicated in the figure. Use Simpson's Rule to estimate the area of the pool.

The widths (in meters) of a kidney-shaped swimming pool were measured at 2-meter intervals as indicated in the figure. Using the trapezoidal rule and Simpson's rule, estimate the surface area of th...

The widths (in meters) of a kidney-shaped swimming pool, measured at 2-meter intervals, are: 0,4.4,5.3,6.2,7.7,6.3, and 0. Use Simpson's Rule to estimate the area of the pool.

Evaluate \int^{14}_0 x\sqrt{196-x^2}\;dx. Then, using the tabulated values, apply the Trapezoidal Rule and Simpson's Rule to obtain estimates of the value. Determine i. the value of the integral di...

1. Evaluate the integral below using the trapezoidal rule. Use sub-interval widths of 1, 0.5, and 0.25, and compare your results with the true value of I=-0.346078. 2. Evaluate the integral below u...

Use Simpson's rule with n = 7 to approximate the value of the integral \int_1^{13} y \, dx

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule: \int_1^4 \sqrt [4]{\ln x} dx, n = 6 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's Rule

Use A) the Trapezoidal Rule, B) the Midpoint Rule, and C) the Simpson's Rule to approximate the integral with the specified value of n up to six decimal places. Integral from 0 to 1 of sqrt(z) e^(-...

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) the Simpson's Rule to approximate the integral \int_{0}^{1} \sqrt z e^{-z} \, dz with the value of n =10 , correct up to six decima...

Evaluate the integral. \displaystyle\int _ { 0 } ^ { 1 } x ^ { 2.5 } \sqrt { ( 2.5 x ^ { 1.5 } ) ^ { 2 } + 1 } d x

Solve by using Simpson's rule: \int_0^2 \sqrt{x^3 + 1} dx, n= 4

Solve by using Simpson's rule: \int_2^4 \frac{1}{x^2 + 1} dx, n = 10

How large should n be If you want the error bound to be below 0.005 for the \int_{0}^{2} \frac{3}{x^2}dx using Simpson's Rule?

Use Simpson's rule to estimate \int_0^2 \frac{1}{8} e^{x^2} \ dx with a maximum error of 0.1.

Determine how many subintervals are required to guarantee accuracy to within 0.00005 using the following rules. (Round your answers up to the next appropriate integer.) Integral from 1 to 9 of ln(s...

The widths (in meters) of a kidney-shaped swimming pool were measured at 7-meter intervals as indicated in the figure. Use the Midpoint Rule with n = 4 to estimate the area S of the pool if a_1 = 1...

Calculate the centroid of the region (use Simpson's rule with n = 20 if necessary) y = x^2 and the line y = 2x for 0 \leq x \leq 2.

The function f(x)=e^-x can be used to generate the following table of unequally spaced data: Evaluate the integral from a=0 to b=0.6 using: (a) analytical means, (b) the trapezoidal rule, (c) a...

Use Simpson's rule to approximate the integral from 1 to 4 of x*ln x dx to within 0.00001.

Use Simpson's rule to approximate integral of x*ln(x) dx from 1 to 4 to within 0.00001.

Use the Error Bound to find the least possible value of N for which Error S_N less than or equal to 1 times 10 to the power of minus 9 in approximating

Use Simpson's Rule to approximate the integral \int_{0}^{1/2} \sin(e^{t/2}) \,dt with the value of n=8 .

Approximate the following integrals using Simpson's Rule. Experiment with values of n to insure that the error is less than 10^{-6}. It is best to compute Simpson's Rule approximations and Trapezoi...

Find the Error resulted from approximation by Simpson's Rule: { \int_0^1 \sqrt{( 1+x^3)} dx } compute the result for n = 8

Use the error formula for the Simpson's rule to find n such that the error in the approximation of \int_3^4 (\frac{1}{x})dx is less than 0.0001

Use Simpson's Rule with n = 10 to approximate the integral \frac{1}{\sqrt 2 \pi} \int_{-2}^2 e^{-\frac{1}{2}x^2} \,dx . Given an upper bound for the error involved in this approximation.

Use Simpson's Rule to approximate the value of the definite integral for n=6. Round your answer to four decimal places. Estimate the error in approximating the integral with n=6.

(a)Approximate the following integral using Simpson's rule. Experiment with values of n to ensure that the error is less than 10^-3 . \int_0^{\pi} \frac {4 \cos x}{\frac {17}{8} - \cos x} dx = \f...

Use Simpson's Rule with n=4 steps to estimate the integral from 0 to 2 of (x^4+7)dx and find the upper bound for the error.

State whether the following statements are true or false and correct the false one: 1) Finite difference method is one of the integration methods. 2) Laplace equation covers all the engineering f...

Estimate the integral integral_0^2 1 / square root x^3 + 4 d x by Simpson's rule using n = 8.

Use n = 4 subdivisions to approximate the value of the integral \int_{0}^{2}\sqrt{4 + x^3} by Simpson's Rule.

Use Simpson's rule to approximate \int_{0}^{\pi}\sin(x)dx with n= 4.

Use Simpson's rule with n=4 to approximate. Keep at least 2 decimal places accuracy. \\ \int_1^5 \frac{\cos x}{x}dx

Use Simpson's rule with n=4 to estimate

If the region shown in the figure is rotated about the y-axis to form a solid, use Simpson's Rule with n= 8 to estimate the volume of the solid.

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) the Simpson Rule to approximate the integral \int_{0}^{1}x^3\ dx; n=6. Round your answers to six decimal places.

1) Let f(x) = e^{-x^2}. The formula for approximating the area between f(x) and the x-axis using Simpson's rule is: S_n =\frac{\Delta x}{3}[f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+........+2f(x_{n-2})+4f(...

A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see the table). Use Simpson's Rule to estimate the distance the runner covered during those 5 seconds. Cho...

Use the table below and Simpson's Rule with n = 10 to approximate \int_0^2 f(x)dx. |x|f(x) |0|2.8

Set up the Integral for the length of the are of the hyperbola xy = 5 from the point (1, 5) to the point (2, 5/2).

Use Simpson rule with __n=10__ to approx the area of the surface obtained by rotating the curve about the X- axis.y=\frac {1}{5}x^5, \ \ 0 \leq x \leq 5\\ Simpson's \ Rule \ \ \Box\\ calculator \ a...

Use Simpson's rule with n=6 to approximate the area of the surface obtained by rotating the curve about x-axis. \\ y=x+\sqrt(x), \ \ 1 \leq x \leq 2

Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exa...

Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the integral for the given value of n. Round the answer to four decimal places and compare the results with the exact value o...

Approximate integral from -1 to 1 of cube root of (x + 1) dx, using the Simpson's rule with n = 8.

Approximate the value of the integral, int_0^2(1+x^3) dx, by using Simpson's rule with the value of n=4.

Use Maple 15 to evaluate the following definite integrals. In each case, find an exact value of the integral (obtained by a symbolic method) and find an approximate value (obtained by a numerical m...

Use Simpson's rule with n = 6 to approximate: integral_1^4 1 / x^2 dx. Give the answer correct to 4 decimal places.

Approximate \ln 5 by choosing the appropriate value of b and approximate the integral below by Simpson's Rule with n=8 Be sure to render your final approximation as a decimal after displaying your...

Consider the following. \int^2_1 \frac {( 7 \ In(x))}{(1+x)} \ dx, n=10 Use Simpson's Rule to approximate the given integral with the specified value of n. (Round your answer to six decimal plac...

Use Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) \int_{0}^{4}\sqrt{1+\sqrt{x}}dx, n=8

Use Simpson's Rule with n = 6 to approximate \pi using the given equation.(Round your answer to five decimal places.) \pi = \int_{0}^{1} \frac{4}{1+x^2} dx

Given the table below. Approximate the total volume of water that passed through the dam from t = 1 to t = 13, with n = 6 using Simpson s rule.

Use "S" as the integral symbol 1) Find the integral f(x)=S(x^2-4x)^3(x-2)dx 2) Find the area (the same problem except the S has a 3 on top and a 1 on the bottom) 3) Find the area using the trapezoi...

Use the Trapezoidal rule, the Midpoint rule and the Simpson's rule to approximate the integral \int_2^6 \frac{3\cos 7x}{x} \,dx with n= 4

Use the Trapezoidal rule, the Midpoint rule, and Simpson's rule to approximate the integral \int_1^4 5 \sqrt{\ln x} \, dx with n = 6

Integration provides a mean to compute how much mass enters or leaves a reactor over a specified time period as in

Approximate the following integral using the Composite Simpson Rule with n = 4, find a bound for the error using error formula and compare this to the actual error: integral_{0.5}^1 x^4 dx.

Use Simpson's Rule with n = 4 steps to estimate the integral and find the upper bound for the error. \int^2_0 (x^4 + 7) dx

Use the error bound to find the smallest value of N for which Error (S_N) less than or equal to 10^{-9} . \int_{1}^{6} x^{4/3} dx N=

Use the error bound to find the smallest value of N for which Error (S_N) \leq 10^{-9} \int_{1}^{0} 7e^{x^2} dx . N=\; \rule{20mm}{.5pt}

Use the error bound to find the smallest value of N for which Error (S_N) \leq 10^ {-9} . \hspace{10mm} \int_{1}^{3} x^{4/3}\; dx N= \;\rule{20mm}{.5pt}

Estimate integral_0^{16} x^2 dx using SIMP(2).

Given the error function erf[x] = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} \, dt . Use Simpson's rule with n = 6 to find erf[3]

The integral 1=\int_{0}^{1}\frac{\sin x}{x}dx is important to design precise photographic lenses (among other applications) The function f(x)= \frac{\sin x}{x} however has no elementary antiderivat...

Use Simpson's rule with n = 4 to approximate ln(8) = integral from 1 to 8 of 1/x dx.

Use Simpson's rule with n = 4 to approximate the integral from 1 to 4 of 1/x^2 dx.

Use Simpson's Rule to approximate the value of the definite integral integral_0^8 2^4 sqrt x dx with n=8.

Use n=4 and Simpson's Rule to approximate the integral \int_{0}^{2} e^{x^2} dx

1. Estimate the definite integral "by hand," Using Simpson's Rule with n = 4. Round all calculations to three decimal places.\int^3_1 4x^2 dx \\ ...............

Apply Simpson's Rule to approximate the value of the definite integral using 4 sub-intervals: integral 4 1 square root 1 + x 3 d x

Use Simpson's Rule to approximate the definite integral of x^3 \cos(x^2)dx from 0 to 2, with n=4.

Use Simpson's Rule to approximate the value of the definite integral \int_0^8 2^4 \sqrt x \ dx \ with \ n = 8. Round your answer to four decimal places. a. 24.5441 b. 16.9283 c. 18.5139 d. 21...

Use the long version of Simpson's Rule to evaluate the following integral when n = 8. integral_0^{16} x^2 dx.

Use Simpson's rule to estimate the value of the integral with the given value of n. integral_1^5 x^2 - x + 1 dx, n = 4.

Use Simpson's Rule, with n=6, to approximate the integral? \int _ { 0 } ^ { 1 } 7 e ^ { - 4 x } d x

Use Simpson's Rule to approximate the given integral with n equals 4. \int_{0}^{2} x^4 dx

Use Simpson's Rule to approximate the given integral with n =4. int_0^2 x^4 dx

Apply Simpson's rule with n=4 and n=8 to evaluate the integral \int_0^8 (8x^5-4x^3) \,dx

Use Simpson's rule to approximate the integral \int_{1}^{4} x \ln x \, dx to within .00001

Use Simpson's rule to approximate the given integral with the specified value of n. int_{1}^{4} ninth root of{ln (x) } dx, n=6.

The values of a function f are as follows: |x |3.0| 3.4 |3.8| 4.2| 4.6 |5.0| 5.4 |f(x)| 4.14 |4.73| 5.29 |5.81| 6.17| 5.84 |5.52 Approximate \int_{3}^{5.4} f(x) dx using Simpson's Rule.

Let f(x) = e^{x^2} . It can be shown by direct computation that f^{(4)}(x) \leq 76e on the interval [0,1] . Using this information and the appropriate error formula, how large should n be so...

Let f(x)=e^x^2 . It can be shown by direct computation that f^(4) (x)leq 76e on the interval [0, 1]. Using this information and the appropriate error formula, how large should n be so that the...

Let f(x)=e^x^2 . It can be shown by direct computation that f^(4) (x)leq 76e on the Interval [0,1]. Using this information and the appropriate error formula, how large should n be so that the S...

Estimate the arc length of y=sin x from x=0 to x=pi to to an accuracy of four decimal places. (Hint Simpson's Rule with n=10). Find the surface area of the volume of revolution generated by revol...

The region bounded by y = 3e^{-4/x}, y=0, x=1, x=5 is rotated about the x-axis. Use Simpson's rule with n = 8 to estimate the volume of the resulting solid.

Using the error formula to estimate the errors in approximating the integral, with n = 8, using a) the Trapezoidal Rule and b) Simpson's Rule. \int^\frac{\pi}{3}_0 3\sin(2x)dx

1. Assuming n=10, approximate the error bound if using Simpson's rule to estimate this integral: \int^1_{-1} e^{-t^2} \ dt Use the error approximation formula for the Simpson's rule.

How do I use error bounds to determine the accuracy of the trapezoidal and simpson's rule? We're using the definite integral \int^1_0sin(x^2)dx

In estimating \int^4_{-1} \cos(2x)dx using Trapezoidal and Simpson's rule with n = 10, we can estimate the error involved in the approximation using the Error Bound formulas. For Trapezoidal ru...

An electronics company analyst has determined that the rate per month t which revenue comes in from the portable GPS division is given by the following formula R(x)=110e^{0.04\sqrt{x}}+23 where x i...

Use Simpson's Rule with n = 6 to estimate the length of the arc of the curve with equations x = t^2, y = t^3, z = t^4, 0 less than or equal to t less than or equal to 3.

Use Simpson's Rule with n = 6 to estimate the length of the curve x = t - e^t, y = t + e^t, - 6 less than or equal to t less than or equal to 6.

Given the following integral and value of, approximate the integral using the methods indicated (round your answers to six decimal places) (a) Trapezoidal Rule (b) Midpoint Rule (c) Simpson's Rule

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve y = \ln(x), 1 \le x \le 3, about the x-axis.

1. Set up the Integral for the length of the arc of the hyperbola xy = 5 from the point (1,5) to the point (2,\frac{5}{2}). 2. Use Simpson's Rule with n = 10 to estimate the arc length.

The planet Pluto travels in an elliptical orbit around the Sun (at one focus). The length of the major axis is 1.18 \times 10^{10} km and the length of the minor axis is 1.14 \times 10^{10} km. Use...

Find the indefinite integral \int \frac {(\frac {5^3}{x} - (x^8 + 9)^{1/3} )}{ 3x^2} dx

Students are required to calculate the drag coefficient C D of the fluid flow across a circular cylinder. The formula for calculating C D is given as: C D = ? ? 0 C p cos ? d ? . " C p cos (...

Given the following graph of the function y = f(x) and n = 6, answer the following questions about the area under the curve from x = 0 to x = 6. 1. Use the Trapezoidal Rule to estimate the area....

Please clear handwriting Use the Simpson's rule for \int_{1}^{3}\frac{ 2}{x} dx. (a) Estimate the integral with n = 10.

Approximate the following definite integral, with the Trapezoidal Rule and Simpson's Rule with n = 6 1 0 x 2 + 1 d x

Approximate the following definite integral, with the Trapezoidal Rule and Simpson's Rule with n = 6 1 0 cos ( x 2 ) d x

Approximate the following integrals using Simpson's rule using the given value of n: \int_0^4 2^x\ dx,\ \ n = 12

The region bounded by the curve y = \frac{2}{(1 + e-x)} , the x- and y-axes, and the line x = 10 is rotated about thex-axis. Use Simpson's Rule with n = 10 to estimate the volume of the resulting s...

The region bounded by the curve y = 4 / {1 + e^{-x}}, the x and y axes, and the line x = 10 is rotated about the x-axis. Use Simpson's Rule with n = 10 to estimate the volume of the resulting solid...

The region bounded by the curve y = 1/(1 + e -x), the x and y-axes, and the line x = 10 is rotated about the x - axis. Use Simpson's Rule with n = 10 to estimate the volume of the resulting solid.

The region bounded by the curve y = 2 / (1 + e^{-x}), the x and y axes, and the line x = 10 is rotated about the x-axis. Use Simpson's Rule with n = 10 to estimate the volume of the resulting solid...

Given integral_{-9}^{9}(-3x^4+5x-9)dx a) Compute the exact values using Fundamental Theorem of Calculus. b) Find the approximate value of the definite integral using the trapezoidal rule with n=9 c...

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) \int_{4}^{6} 6 \ln(x^3...

Evaluate the integral. t = \int_{0}^{3} (ds/( (2.78s + 0.8s^{3})^{1/2} ))

Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. (Round your answers to six decimal places.) y =...

Use the 3 step method to find the length of the curve y = sin x where 0 leq x leq pi.

Use Simpson's rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.) x...

Use Simpson rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.) y =...

Use Simpson?s Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. y = x \sin x, 0 \leq x \leq 2\pi.

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.) y...

Use Simpson's with n=10 to estimate the arc length of the curve. Compare the answer with the value of the integral produced by the calculator. (Round the answer to six decimal places.) y= x\sin...

Find n such that the error in approximating the given definite integral is less than 0.0001 when using: a. Trapezoidal Rule b. Simpson's Rule \int_0^{\pi} \sin x \ dx

Find n such that the error in approximating the given definite integral \int_0^5 x^4 \ dx is less than 0.0001 when using: a. Trapezoidal Rule b. Simpson's Rule

Find n such that the error in approximating the given definite integral \int_1^4 \frac{1}{\sqrt x} \ dx is less than 0.0001 when using: a. Trapezoidal Rule b. Simpson's Rule

Suppose that the accompanying table shows the velocity of a car every second for 8 seconds. Use Simpson's Rule to approximate the distance traveled by the car in the 8 seconds. Round your answer to...

Approximate the following integrals using Simpson's rule using the given value of n: \int_2^6 \dfrac{dx}{x + 3},\ \ n = 10

Use Simpson's Rule with n = 4 steps to estimate the integral. \int_{-1}^{1}(x^{2}+7)dx

Find an approximate value for the integral, using Simpson's rule with n intervals.\\ \int_0^1 \frac{1}{1+x^2} dx, \ n=4 \\ A) 5323/6800 \\ B) 5323/3400 \\ C) 8011/10200 \\ D) 8011/5100

Find: Use Simpson's method with n=4 to approximate \int_0^8 f(x) dx where y=f(x) is given by the graph below. Image src='img_22082019_202247_448_x_500_pixel5654188452921282223.jpg' alt='' caption=''

Use Simpson's Rule with __n=4__ step to estimate the integral. \int^2_0 \ (x^4+7)dx

Use the Simpson's rule, n=3, to estimate the interval of \frac{(\sin x)}{(\pi + x)} dx on the interval (0, pi).

Approximate the following integrals using Simpson's rule using the given value of n: a) \int_0^4 2^x dx, n = 12 \\ b) \int_2^6\frac{dx}{x + 3}, n = 10

Estimate the integral int_{0}^{3} frac{1}{sqrt{x^3 + 5}} dx| by Simpson's rule using n = 8.

Find an approximate value for the integral, using Simpson's rule with n intervals. \int^4_0 (51x^2 + 17) dx, n = 4 A. 1,309 B. 1,156 C. 1,173 D. 68

Find an approximate value for the integral , using Simpson's rule with n intervals ... \int ^4_0 (12x^2+4) dx , n=4.

Evaluate the definite integral. I am supposed to do it with substitution but don't know what to substitute for this problem. \int^4_1 ( \frac {e^{4x} }{ x^2} ) dx

Evaluate the integral from 1 to 10 for the following data by employing. i. Trapezoidal rule ii.The best combination of trapezoidal and Simpson's rules

Sketch the graph of a continuous function on (0, 2) for which the Trapezoidal Rule with n = 2 is more accurate than the Midpoint Rule.

(a) Use the Midpoint Rule and the given data to estimate the value of the integral I. (Give the answer to two decimal places.) I = \int^{3.2}_0f(x) dx 24.84 |x|f(x)|x|f(x) |0.0|7.6|2.0|8.1 |0.4|8.5...

Use Simpson's Rule and the Trapezoid Rule to estimate the value of the integral \int_{-3}^3(2x^3 - 2x^2 - x - 3)dx In both cases, use n = 2 subdivisions Simpson's Rule approximation S_2 = [{Blan...

Apply Simpson's rule to the following integral. It is easiest to obtain the Simpson's rule approximation from the trapezoid rule approximations. Make a table showing the approximation and errors fo...

You can use the formula for Simpsons Rule given above; but here is a better way. If you already have the Trapezoid Rule approximations T(2n) and T(n), the next Simpson's Rule approximation follows...

Use Simpson's rule: \int_{2}^{4}\frac{1}{x^{2}+1}dx, n=10

Use parametric equations and Simpson's Rule with n = 8 to estimate the circumference of the ellipse 9x^2 + 4y^2 = 36.

Estimate the value of the integral ? 8 2 x e ? x 2 d x using three different approximations. (a) Calculate the approximate value of the integral using the trapezoidal rule. (b) Calculate the ap...

Find the length of the curve y=sin x, 0leq x leq pi using the 3-step method.

Use the Midpoint Rule with n=4 to approximate \int_0^{\pi/4} \tan x \, dx

Find SIMP(2) for the definite integral below. \int_{0}^{4}x^{2}dx

State True or False and justify your answer: A high number for the Simpson's index of diversity indicates that there is a large diversity of species present in an ecosystem.

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. (Give your answers correct to 4 decimal plac...

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integral_{0}^{2} square root {x^2+1} dx

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integral_{-3}^{1} e^{x^2} dx

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integral_{1}^{-1} 1/sin x+2 dx

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integral_{1}^{4} In x dx

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integra_{0}^{x} x sin x dx

In approximate the definite integral with the Trapezoidal Rule and Simpson's Rule, with n=6. Integral_{0}^{1} cos(x^2) dx

Find the upper bound on the errors in Simpson's rule for the function integral from \int_{1}^{3}(1/\sqrt{x+1})dx

consider the definite integral { \int_0^4 cos(x^4) dx } a) Use the Trapezoidal Rule with n =8 to approximate the integral. b) Use Simpson?s Rule with n = 8 to approximate the integral. c) Whic...

Estimate the integral from 0 to 1 of 13cos(x^2) dx using the trapezoidal rule and the midpoint rule, each with n = 4. (Round your answer to six decimal places.)

The fuel tanks for airplanes are in the wings, cross section below. The tank must hold 5400 lb of fuel with density 42 lb/ft^3. Estimate the length of the tank using Simpson's Rule.

The fuel tanks for airplanes are in the wings, cross section below. The tank must hold 6000 lb of fuel with density 42 lb/ft^3. Estimate the length of the tank using Simpson's Rule.

Evaluate the integral. int \frac{e^{2x + 1} - e^{2x}}{-3x^x} + \sqrt x

User Simpson's Rule with n = 8 to estimate the length of the curve y = x^{2}e^{x} on 0\leq x\leq2

The portion of the graph y=\tan^{-1}x between x= 0 and x=1 is rotated around the y-axis to form a container. The container is filled with water. Use n=6 subintervals and Simpson's rule to approxima...

1. Calculate S_N given by Simpson's Rule for the value of N indicated. (Round your answer to five decimal places.) \int_0^3 \frac {dx}{x^2+3}, N=6

Calculate S_N given by Simpson's Rule for the value of N indicated. integral_0^3 dx/x^3 + 3, N = 6

Calculate S_N given by Simpson's Rule for the value of N indicated. \int_0^3 \frac{1}{x^3 + 7}dx, N = 6

Calculate S_{N} given by Simpson's Rule for the value of N indicated. (Round your answer to three decimal places.) \int_{2}^{5}\sqrt{x^{4}+3}dx, N=4

Calculate S_N given Simpson?s Rule for the value of N indicated. (Round your answer to five decimal pales.) \int_{0}^{3} \frac{dx}{x^2+7} , \; N=6

Use Simpson's Rule with n = 4 steps to estimate the integral and find the upper boundary. integral 2 0 ( x 4 + 7 ) d x

Consider the integral from 0 to pi/2 of sqrt(sin x) dx. Write an expression that approximates the integral, with n = 6, and evaluate that expression, using the Simpson's Rule.

Estimate the area under the graph of f(x)=e^{-6x^2} from x=0 \enspace to \enspace x=2 using the midpoint rule with n=4.

Use Simpson's Rule to approximate \int_{1.0}^{2.8} f(x) dx using the following data points. |x |1.0 |1.3 |1.6 |1.9 |2.2 |2.5 |2.8 |f(x) |3.2 |4.1 |5.2 |4.6 |4.2 |5.1 |5.7

Use Simpson's Rule and all the data in the following table to estimate the value of ? ? 10 ? 16 y d x x -16 -15 -14 -13 -12 -11 -10 y 0 -3 -9 9 -1 9 5

Use Simpson's rule and the data in the following table to estimate the value of \int_{27}^{33} y \, dx | x | 27 | 28 | 29 | 30 | 31 | 32 | 33 | y | -7 | -9 | -9 | -8 | -5 | -5 | 0

Use Simpson's Rule and all the data in the following table to estimate the value of \int_{-13}^{-7} y dx. <table> <tr> <th>x</th> <th>-13</th> <th>-12</th> <th>-11</th> <th>-...

Use Simpson's Rule and all the data in the following table to estimate the value of \int_{-5}^1 y dx. Answer:

Given int 0 4 sqrt(x) dx. Approximate the definite integral with the Simpson's Rule and n = 4.

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. \int_1^3 (4 - x^2)dx, n = 4.

Compute the approximate value (to four decimal places) of the following definite integral using both the Trapezoid Rule and Simpson's Rule. \int_0^2 e^x dx, n = 4

Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Integral from 0 to sqrt(pi/2) of sin(x^2) dx.

Use Simpson rule to estimate Arc length of the graph. (y-1)^{3}=X^{2} when n=8, interval 0 \leq \ x \leq 8

Find or evaluate the following indefinite and definite integral. \int \frac{x + 2}{\sqrt{4 - x^3}} dx

Use the Trapezoidal Rule and Simpson's Rule to approximate the results with the exact value of the definite integral. \int_{1}^{2} \left ( \frac{x^2}{4} + 6 \right ) dx, n = 4 Exact: Trapezoidal: S...

Evaluate \int_2^{10} 3xdx using the trapezoidal rule and Simpson's rule. Determine: 1. The value of the integral directly. 2. The trapezoidal rule estimate for n = 4. 3. An upper bound for |E_T|...

How large should n be to guarantee that the Simpsons rule approximation to integral 0 to 1 7 e^x^2 is accurate to with in 0.00001?

A surveyor measured the length of a piece of land at 100-ft intervals (x), as shown in the table. Use Simpson's Rule to estimate the area of the piece of land in square feet. x Length (ft) 0 50...

Find the best quadratic approximation for \sqrt(16+32x-y) for (x,y) near (0,0).

Use Simpson's Rule with n = 4 to estimate the arc length of the curve y=e^{-2x}, 0 \leq x \leq 2. L = \int_0^2 f(x)dx where f(x) = The estimation S_4 = .

Approximate F(x) for x = 0, 0.5, 1, 1.5, 2, 2.5. F(x) = \int^x_0\sin(t^2)dt Round your answers to three decimal places. F(0) = _____ F(0.5) = _____ F(1) = _____ F(1.5) = _____ F(2) = _____ F(2...

Use Simpson's rule with n = 4 to approximate integral_1^5 {cos x} / x dx.

Use the Simpson's rule to calculate I = \int_{0}^{\pi} e^{\pi} \cos (x) dx.

Approximate \int_{0}^{2}(x^{2} + 1)dx with n = 4 subintervals, using Simpson's rule.

Estimate the area under the graph in the figure by using a. Trapezoidal Rule b. The Midpoint Rule c. Simpson's Rule each with n = 4. (Graph)

Find: Estimate the area between x=0 and x=4 under the graph in the figure by using a) the Trapezoidal Rule b) the Midpoint Rule c) Simpson's Rule each with n = 4. What observations c...

Estimate the area under the graph in the figure by using (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule, each with n=4. Trap(4) = Mid(4)= Simpson(4)=

Find the area under the semicircle y = \sqrt{144 - x^2} and above the x-axis by using n = 8 by using the following methods. a. Trapezoidal rule b. Simpson's rule Compare the results with the area f...

Integrate (lim: 0 to 2pi) 2 s i n^x e^x d x Using the integral above, approximate the area using the Trapezoid rule with 4 subdivisions, and the Simpson's Rule with 4 subdivisions.

(a) Use Simpson's Rule, with n=6, to approximate the integral integral_0^1 8e^{-3x} dx. S_6= (b) The actual value of integral_0^1 8e ^{-3x} dx= (c) The error involved in the approximation of part (...

(a) Use Simpson's Rule with n = 4 subintervals to estimate \int_1^9 \sqrt{x} \ dx. (b) Use the Error Bound to find the bound for the error. (c) Compute the integral exactly. (d) Verify the error...

Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. (Give your answers correct to 4 decimal places.) \int_{0}^{3}4(1+x^{3})^{1/2};n=4

Use the Trapezoidal and Simpson's rule to approximate the value of the definite integral? \int _1^6 5(x^2-1) dx, n=4. Compare your result with the exact value of the integral. (Give your answers c...

Evaluate Integral integral_2^{10} 2 / s^2 ds using the trapezoidal rule and Simpson's rule. Determine i. the value of the integral directly. ii. the trapezoidal rule estimate for n = 4. iii. an up...

The length or one arch of the curve y=sin (x) is given by L=integral _0^pi square root {1+cos^2(x)} dx Estimate L by Simpson's Rule with n=6. L approx

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