Let R denote the region inside x^2 + y^2 = 1 but outside x^2 + y^2 = 2y with x=>0 and y=>0. Let u=x^2 + y^2 and v=x^2 + y^2 -2y. Compute the integral of x*e^y over the region D in the uv-plane which corresponds to R under the specified change of coordinates. I'm having trouble with this one. My first attempt at figuring out the new limits of integration yielded 0<=u<=1 and 0<=v<=u, which seems wrong to me. I'm also not sure how to change the integrand to make it a function of u and v.