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$\phi$d$\rho$d$\theta$d$\theta$ -$\int^{2\pi}_{0}$ $\int^{\pi/4}_{0}$ $\int^{1/sin\phi}_{0}$ $\rho^{2}$sin$\phi$d$\rho$d$\phi$d$\theta$

is this correct?

 

[whynot314]

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