Chapter 8, Problem 69RE

### 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 69-74, evaluate the definite integral using any method. Use a graphing utility to verify your result. ∫ 2 5 x ( x 2 − 4 ) 3 / 2 d x

To determine

To calculate: The value and verify the result using a graphing utility of definite integral 25x(x24)3/2dx.

Explanation

Given: We are given with the Definite Integral âˆ«25x(x2âˆ’4)3/2dx.

Formula used:

Substitution method.

Calculation:

Let I=âˆ«25x(x2âˆ’4)3/2dx

Put x2=t

On Differentiating both sides, we get that:

2xdx=dt

xâ†’2,â€‰tâ†’4â€‰â€‰andâ€‹â€‰xâ†’5,â€‰tâ†’5

On substituting, we get that:

I=12âˆ«45(tâˆ’4)3/2dt=12(25(tâˆ’4)5/2)45=15((1)5/2âˆ’0)=0

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started