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Find F as a function of x and evaluate it at x = 3, x = 5, and x = 9 if F(x) = \int_3^x - 2/t^3...

Question:

Find F as a function of x and evaluate it at x = 3, x = 5, and x = 9 if

F(x) = {eq}\int_3^x - 2/t^3 dt {/eq}

F(x) = ?

F(3) = ?

F(5) = ?

F(9) = ?

Integral at a Point:

Firstly, we need to integrate the given expression by the power rule of infinite integrals.

{eq}\displaystyle \int x^{k}\ dx=\frac{x^{k+1}}{k+1}+C {/eq}

Where,

  • {eq}C {/eq} is the constant of integration.

After that, compute the boundaries of definite integral to change the variable of integral and then plug the values of variables to get the exact value.

Answer and Explanation: 1

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Given:

{eq}F(x) =\displaystyle \int_3^x - 2/t^3 dt {/eq}

The definite integral by power rule of integrals is:

{eq}\begin{align*} F(x)...

See full answer below.


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Evaluating Definite Integrals Using the Fundamental Theorem

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Chapter 16 / Lesson 2
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In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.


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