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November 26th, 2012, 02:05 PM   #1
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Double Integral Problem

Hey everyone,

I am having a bit of difficulty with a particular double integral problem. It is the integral of:

(x-y)/(x+y)^3 dydx ; where [x=0 to x=2] and [y=0 to y=1]

How would I solve this problem with respect to y first? I've thought about using partial fractions, but I am not quite sure as to how to apply it within this particular problem. Is there perhaps another method?

Any feedback and help is appreciated, thanks.
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November 26th, 2012, 02:59 PM   #2
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Re: Double Integral Problem

It really doesn't matter whether you integrate with respect to x and y first, it's clear they calculations will be basically the same. You have


No, you would not use "partial fractions" because you already have a linear term over the third power. Instead, make the substitution u= x+ y. The dy= du, when y= 0, u= x, when y= 1, u= x+ 1, and y= u- x so that . The integral becomes
.
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November 26th, 2012, 03:44 PM   #3
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Re: Double Integral Problem

Nice, thanks for the explanation.
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