1. The problem statement, all variables and given/known data Hey guys, I have one question: how can I integrate the function f(x,y,z)=x + y + z over the region between the paraboloid 4-x^2-y^2 and the xy-plane? 2. Relevant equations For the paraboloid region, I used polar coordinates and found the volume of the region to be 8pi. Now, I have to find the integration of the other function x+y+z in this. 3. The attempt at a solution Alright, I tried using a triple integral to no avail (rcos([tex]\theta[/tex]) +rsin(theta) +z)r drd(theta) dz. I do not know the limits of integration (hardest part of the problem for me). Is there anyway to solve this with only a double integral? Or would I have to use cylindrical/polar whatever triple integration to solve it? Thanks..!