Could someone go through this step step by step?

I get stuck at part ii

http://img814.imageshack.us/img814/2227/mathse.jpg

Thanks

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- Jan 16th 2011, 08:41 AMbilledouble integrals
Could someone go through this step step by step?

I get stuck at part ii

http://img814.imageshack.us/img814/2227/mathse.jpg

Thanks - Jan 16th 2011, 10:45 AMOpalg
Assuming that you have done part (i), the essential next step is to draw a diagram of the domain D. That should enable you to describe D in terms of u and v, namely that D is enclosed by the lines , , and . The change of variables formula then tells you that the integral is equal to

. . . . . .

The " "s conveniently cancel, and from then on the integral should be easy. - Jan 16th 2011, 10:48 AMbille
Sorry, what is the change of variable formula?

Thanks for our reply. - Jan 16th 2011, 11:10 AMOpalg
The formula says that if you make a change of variables from (x,y) to (u,v), so that f(x,y) becomes g(u,v), then the integral becomes .

See here for more on this topic. (But if you are being asked to do problems like this, then presumably it is expected that you already know this stuff.)