1. The problem statement, all variables and given/known data The region between sphere x^2+y^2+z^2=3 and the upper sheet of the hyperboloid z^2=x^2+y2+1. 2. Relevant equations 3. The attempt at a solution Curve of intersection: We set the two equations equal to each other and find x^2+y^2=1, a circle of radius 1 is the curve of intersection. I then drew the graph of the two elements here. Now, I need to set up the actual double integral. I know my bounds: theta from 0 to 2pi and r from 0 to 1. I know that using polar coordinates I have to use r*dr*d(theta). My problem is, I don't know how to set up the rest of the integral. I think it has something to do with f(r,theta)-g(r,theta) but I've been trying various things and nothing seems to be clear/working out. I think I should do (3-x^2-y^2) - (x^2+y^2+1) as that seems to be the correct order, but how do I switch this to polar coordinates :/.