# question about integrating over an ellipse?

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• Jan 25th 2010, 09:00 AM
sue
question about integrating over an ellipse?
integrate f(x,y)=xy over the ellipse (x/4)^2 + (y/2)^2 which is less than or equal to 1 .
Do this by first changing variable, u= x/4 , v= y/2 .

Please help. Thanks ! :)
• Jan 25th 2010, 09:33 AM
Krizalid
Yes, that's all, now it's easy to check that $8\,du\,dv=dx\,dy$ and your region is the circle $u^2+v^2\le1,$ so the common polar transformation will do the job.
• Jan 26th 2010, 05:22 AM
sue
Quote:

Originally Posted by Krizalid
Yes, that's all, now it's easy to check that $8\,du\,dv=dx\,dy$ and your region is the circle $u^2+v^2\le1,$ so the common polar transformation will do the job.

can u explain more please?
• Jan 26th 2010, 05:23 AM
Krizalid
I don't know, from there it's clear.

I'd like to know what you don't get.