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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

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.

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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Chapter 14 Solutions

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