To find the boundaries of integration, we find where the two surfaces intersect. For instance,
which means that our two paraboloids intersect in a circle of radius . Our integral is therefore
I'm having trouble with the following problems:
1.) Find the volume of the region bounded by the paraboloids z = 2x^2 +y^2 and z= 12 -x^2 -2y^2
2.) Find the volume of the region bounded above by the spherical surface x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 +y^2
Can someone give an explanation of what the boundaires would be for triple integration in cylindrical coordiantes