   Chapter 5.5, Problem 77E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Evaluate ∫ − 2 2 ( x + 3 ) 4 − x 2   d x by writing it as a sum of two integrals and interpreting one of those integrals in terms of an area.

To determine

To evaluate: The integral function 22(x+3)4x2dx.

Explanation

Given:

The integral function is 22(x+3)4x2dx.

The region lies between x=2 and x=2.

Show the theorem 7 (Integrals of symmetric Functions):

Apply the condition as follows if f is continuous on [–a, a].

1. a) If f is even [f(x)=f(x)], then aaf(x)dx=20af(x)dx.
2. b) If f is odd [f(x)=f(x)], then aaf(x)dx=0.

Calculation:

The integral function is,

22(x+3)4x2dx=22x4x2+34x2dx=22x4x2dx+2234x2dx (1)

Consider I1 and I2 as follows:

I1=22x4x2dx (2)

I2=2234x2dx (3)

Substitute I1 for 22x4x2dx and I2 for 2234x2dx in Equation (1)

### 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

#### Simplify the expressions in Exercises 97106. x1/2yx2y3/2

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 63-68, rationalize the denominator. 64. 3xy

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Given: VP Construct: VW such that VW=4VP

Elementary Geometry For College Students, 7e

#### The area of the region at the right is:

Study Guide for Stewart's Multivariable Calculus, 8th 