1. ## 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 .

2. 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.

3. 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.

4. I don't know, from there it's clear.

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