November 26th, 2012, 01:05 PM  #1 
Member Joined: Sep 2012 Posts: 34 Thanks: 0  Double Integral Problem
Hey everyone, I am having a bit of difficulty with a particular double integral problem. It is the integral of: (xy)/(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. 
November 26th, 2012, 01:59 PM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  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 . 
November 26th, 2012, 02:44 PM  #3 
Member Joined: Sep 2012 Posts: 34 Thanks: 0  Re: Double Integral Problem
Nice, thanks for the explanation.


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