I need a little help with the following question:

find the region , bounded by the ellipse in the first quadrant.

I drew out the bounds which gave me a function where and .

now if I let and I would get:

and

so my value associated to the Jacobian transformation would be:

the bounds associated with both and are and

so putting everything together yields:

now this is the part that I get stuck on since doesn't integrate nicely, and checking out my work on maple gives me a bizarre result.