Chapter 4.4, Problem 63E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Evaluating a Definite Integral In Exercises 63 and 64, find F as a function of x and evaluate it at x = 2 ,     x = 5 , and x = 8 . F ( x ) = ∫ 1 x 20 v 2 d v

To determine

To calculate: The function F in terms of x. Then find value of function F(v)=1x20v2dv at x=2,5,8.

Explanation

Given:

The function,

F(v)=âˆ«1x20v2dv.

Formula used:

The integration of type xn are solved as

f(x)=âˆ«xndx=xn+1n+1

Calculation:

The function F(v) can be made into F(x) by solving the integral

âˆ«1x20v2dv=âˆ«1x20vâˆ’2dv=20[vâˆ’1âˆ’1]0x=âˆ’20(1xâˆ’1)F(x)=20(1âˆ’1x)

We will substitute x=2 to calculate F(2)

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