Find the volume of the region between the two paraboloids z1=2x2+2y2-2 and z2=10-x2-y2 using Cartesian coordinates. I let z1 = z2 and solved this to get the intersection of the two paraboloids which gave y2+x2=4 (Which I can also use as my domain for integration?) So the volume of the area between them would be the double integral of z2-z1 dA (where dA = dxdy) x goes from -(4-y2)1/2 to (4-y2)1/2 and y goes from -2 to 2. so integrating z2-z1 with respect to x first and plugging in the terminals (after some algebra which I hope I've done right) condenses to 4(4-y2)3/2 now I need to integrate this with respect to y from -2 to 2. I don't know how to solve that integral, I've tried parts and looking up tables. If I've stuffed up somewhere or have done this completely wrong any help would be greatly appreciated.