spherical coordinates: volume of region bounded by graphs

[mammothrob]

I have to find the volume of the region bounded by the graphs in spherical coordinates.

I have x2 + y2 +z2 = 2, which converts to p= sqrt(2) [sphere]

and z = x2 + y2 which I converted to cot(phi)csc(phi) = p [parabloid]

Im having trouble setting up the triple

V= SSS dp d(theta) d(phi)
R
any hints or even a set up would be helpfull.
thanx

 

[galactus]

I assume your bounded above by the sphere and below by the paraboloid?.

HINT: Here's the integral in cylindrical coordinates. If you set your spherical up correctly, you should get the same thing.

\(\displaystyle \L\\\int_{0}^{2{\pi}}\int_{0}^{1}\int_{r^{2}}^{\sqrt{2-r^{2}}}rdzdrd{\theta}=\frac{(8\sqrt{2}-7){\pi}}{6}\)