Triple integral volume of solid (set up)

[whynot314]

Homework Statement

I need help setting this integral up in spherical coordinates, the region above the xyplane, inside the sphere x^2+y^2+z^2=2 and outside the cylinder x^2+y^2=2

The Attempt at a Solution

\int^{2\pi}_{0} \int^{\pi/2}_{\pi/4} \int^{\sqrt{2}}_{0} \rho^{2}sin\phid\rhod\thetad\theta -\int^{2\pi}_{0} \int^{\pi/4}_{0} \int^{1/sin\phi}_{0} \rho^{2}sin\phid\rhod\phid\theta

is this correct?

 

[whynot314]

cylinder is x^2+y^2=1 oops, and on first integrand its drho,dphi,dtheta.