## Antiderivative Questions and Answers

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Evaluate the following integral: \int \frac{x}{\sqrt{x^2 4}} \text{d} x

Solve \int \sec^n x dx for n0

Find the antiderivative of e^{-0.5t} + 1

Evaluate the indefinite integral \int_0^4 (2e^x+3 \sin x) dx

Evaluate the indefinite integral \int \frac {8-3xe^x}{x} dx

Evaluate the indefinite integral \int \frac {du}{4\sqrt u}

Evaluate the indefinite integral \int x(4+3x^4)dx

Given that f''(x)=\cos (x), f' \frac {\pi}{2}=14, f \frac {\pi}{2}=12, find f'(x) and f(x).

Evaluate the indefinite integral \int (4x^2+4x-6) dx

First find f' and then find f. f''(x) = 2x^3+3x^2+10 f'(1)=-9 f(1)=-5 f(x)=? f(x)=?

Evaluate the following indefinite integral \int (x+9)^{-4} dx

Find the integral \int \frac{x-3}{\sqrt{x^2 + 1}} \,dx

Find the integral \int \frac{\sec^2 x}{25 - \tan^2 x} \,dx

Find the following integrals: a) \int (4x^2 - 1)\,dx b) \int (\sqrt x - \frac 2x)\, dx

Use the indicated technique to evaluate the following integral. Show work detail to support your solutions. Solving using other methods or with no detail is not acceptable. \int \frac{x^{2}}{\sqrt{16 - x^{2}}} dx (Trigonometric substitution)

Evaluate the integral by making an appropriate substitution. \int \tan x \sec^{4} x dx

Evaluate the integral by making an appropriate substitution. \int\frac{x}{x^{2} + 4} dx

Show that if f(x) is the antiderivative of v(x) then f(2x) is the antiderivative of v(2x) .

Find the most general antiderivative or indefinite integral. ? 3 + 4 x 1 + x 2 d x

Find the most general antiderivative or indefinite integral. ? d x ? 1 ? x 2 sin ? 1 x

Find the most general antiderivative or indefinite integral. ? tan ? 1 x x 2 + 1 d x

Find the most general antiderivative or indefinite integral. ? ln 6 ( x ) x d x

Find the most general antiderivative or indefinite integral. ? 56 x ( 6 ? e x ) 2 d x

Find the most general antiderivative or indefinite integral. ? 4 + ? x + 5 x x d x

State whether the following statement is true or false. If it is false, correct the statement and explain why it is not true, or give a counter example. The most general anti derivative of f(x) = x^{-2} is F(x) = -\frac{1}{x} + C

Find the most general anti derivative of f(x) = 6x^2 + 3e^x + 8x + 5\sin x+ 3

Suppose F_1 and F_2 are both anti derivatives of f on an interval I . How are F_1 and F_2 related?

What is an anti derivative of a function f(x) ?

Evaluate the indefinite integral \int \frac{6x^3 + 4x^2 + 2}{x^2} \,dx

Given that f'(x) = \frac{8}{5}x^{3/5} . Find f(x)

Find the anti derivative of f(x) = 1 + x + \sin(3x)

Find the anti derivative of f(x) = 10x^4 + 12x^5

Evaluate the integral \int \frac{9}{x(\ln(7x))^7} \,dx

Determine the integral \int \frac{6}{x\sqrt{x^2+9}} \, dx

Evaluate the indefinite integral of (e^(-Beta)(r))/(r)(dr)

Verify that F(x) is an antiderivative of the integrand f(x) and use Fundamental Theorem to evaluate the definite integral. \int _1^7 \sqrt x \ dx, \ F(x) = \frac{2}{3}x^{3/2}

Evaluate the given interval \int 6t^3+8t^{?6}+t^{?10}dt

Evaluate the given interval \int 5z^{?4}+5z^4?9dz

Find the indefinite integral. \int \sqrt{7x + 12} dx =

Find the indefinite integral. \int \sqrt{t(t^2 + t - 1)} dt

Find the indefinite integral. \int (2 + x + 2x^2 + e^x)dx

Find the indefinite integrals: a. \int (x^2 - x + 2)\,dx b. \int (\frac 1x + 5e^x)\,dx c. \int (\sqrt[3]{x^2} + \frac1{x^2})\,dx d. \int (2x+3)(3x-1)\,dx (Hint: Multiply first before integrating) e. \int (frac {2x^2 -5x+1}{x})\,dx (Hint: Divide first befo

If consumption is $2.9 billion when income is $1 billion and if the marginal propensity to consume is dC/dy = 0.5 + 0.2/sqrt(y) (in billions of dollars), find the national consumption function C(y).

A company is considering a new manufacturing process in one of its plants in an effort to save money. The company estimates that the rate of savings can be modeled by S(x) = 100 - x^2 where x is time in years and S(x) is given in thousands of dollars pe

(a) For a given function f, what is the difference between antiderivative of f and indefinite integral of f? (b) If we first differentiate and then integrate, do we again obtain the same function? In other words, is it correct that \int f'(x) dx = f(x) f

A flu epidemics hits a college community, beginning with five cases on day t=0. The rate of growth of the epidemic (new cases per day) is given by the function r(t) = 18 e^{0.05 t}, where t is the number of days since the epidemic began. a. Find a formula

A virus is spreading at a rate of r(t)=20e^{0.04 t} cases per day. The virus started with 5 cases on day t=0. a. Find the formula for the total number of flu cases in t days, b. Find the total number of cases in the first 20 days.

Which one of the following statement are true: a. If f(x)=-5, then the general anti-derivative of f(x) is 5x+2 b. If f(x)=-5, then the particular anti-derivative of f(x) is 5x+C c. If f(x)=-5, then the particular anti-derivative of f(x) is 5x+3 d. If f(x)

Find the antiderivative of g(x)=2x which contains the point (2,0)

Rewrite f(x) as f(u) using a substitution of variables f(x)= \int x \cos (4x^2-6) dx

Find f(x)= \int \left ( \frac{2}{x+2}+2^x \right ) dx

Find f(x) = \int \frac{2}{\sqrt {x+4} dx

Determine the indefinite integral value. \int \frac{x^3 - 4x}{(x^2 + 1)^2} dx|

Determine the indefinite integral value. \int \frac{2x + 21}{2x^2 + 9x - 5} dx

Find the indefinite integral of the following function and check the result by differentiation. \int (5-z)\sqrt{z}dz

Evaluate the integral: \int 2x^{-9}+12x^{-5}+7x^{-3}-x^{-2} \ dx

Evaluate the integral: \int 10z^{-6}+8z^{-5}-z^{-2}+1 \ dz

Evaluate the integral: \int 4 \ dw

Evaluate the integral: \int -7 \ dz

Determine the integral \int x^9-6x^4-21x^2-1+9x \ dx