# 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.

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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)...

Evaluating Definite Integrals Using the Fundamental Theorem

from

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.