Chapter 14, Problem 6PS

### 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 Double IntegralEvaluate the integral ∫ 0 ∞ ∫ 0 ∞ 1 ( 1 + x 2 + y 2 ) 2   d x   d y .

To determine

To calculate: Find integrals for the double integral 001(1+x2+y2)2dxdy

Explanation

Given:

As we know the given integral is.

âˆ«0âˆžâˆ«0âˆž1(1+x2+y2)2dxdy

Formula used:

[F(x)]ab=F(b)âˆ’F(a)

cos2Î¸+sin2Î¸=1

Calculation:

First let us consider the given integral

I=âˆ«0âˆžâˆ«0âˆž1(1+x2+y2)2dxdy

Convert into polar coordinates

x=rcosÎ¸,y=rsinÎ¸,â€‰â€‰dxdy=rdÎ¸dr.

Then,

I=âˆ«0âˆžâˆ«0Ï€/2r(1+r2cos2Î¸+r2sin2Î¸)2dÎ¸dr=âˆ«0âˆžâˆ«0Ï€/2r(

### 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