The book prescribes the transformation T(u,v) = (u2 - v2, 2uv) where x = u2 - v2 and y = 2uv. Using this information, I have found that the Jacobian of the transformation as 4(u2 + v2), resulting in the following:
I am just unable to find R, the region of integration. I graphed it in the xy plane looked like a the tip of a leaf protruding over the x-axis.
My biggest problem is that this is not a linear transformation and my professor hasn't taught us how to tackle those.
Any help will be greatly appreciated,