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

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

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