Originally Posted by
MathTooHard Find the double integral of y(e^x) over the region in the first quadrant enclosed by the circle x^2+y^2=25.
For this problem, I think I set up the integral properly, with the radius going from 0 to 5, and the angle going from 0 to pi/2. I set y=r*sin(theta) and x=r*cos(theta), but the first antiderivative from tabular integration by parts (w.r.t. r), was very messy, and the second antiderivative w.r.t. theta looks to be messy as well. I'm not sure whether to keep on brute forcing it, or whether there is a more elegant solution.
I would appreciate any help. Mathematica returns 4e^5 - 23/2 as the answer by the way.