Consider the region bound by
x^2 +y ^2 +z^2 = 4 and the cone z=-\sqrt(x^2+y^2) with -\sqrt2\leqslant z\leqslant 0

In spherical co-ords have i set up the correct bounds?

\int_{0}^{(3\pi /4)}\int_{0}^{(2\pi)}\int _{0}^{\sqrt{2}} r^2\sin \theta drd\theta d\varphi