Question

find the volume of the solid by double integration in polar coordinates: the solid lies inside of the cylinder x^2+y^2=4, above the xy-plane, and below the plane z=4-x-y

Answer 1

This problem is definitely not a double-integral setup, for the same reasons as in your previous question. The fact that you're given a cylinder should be an immediate hint that you should use cylindrical coordinates, not to mention the fact that you're in 3-space.

Answer 2

I just went to my professor's office hours and we solved the problem... it was a double integration problem, not too hard with his help.