   Chapter 14, Problem 6PS

Chapter
Section
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.

001(1+x2+y2)2dxdy

Formula used:

[F(x)]ab=F(b)F(a)

cos2θ+sin2θ=1

Calculation:

First let us consider the given integral

I=001(1+x2+y2)2dxdy

Convert into polar coordinates

x=rcosθ,y=rsinθ,dxdy=rdθdr.

Then,

I=00π/2r(1+r2cos2θ+r2sin2θ)2dθdr=00π/2r(

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