# Substituting spherical coordinates to evaluate an integral

I have to evaluate

$$\int^1_{-1} \int^{ \sqrt {1-x^2}}_{ - \sqrt {1-x^2}} \int^1_{-\sqrt{x^2+y^2}}dzdydx$$

using spherical coordinates.

This is what I have come up with

$$\int^1_{0} \int^{ 2\pi}_0 \int^{3\pi/4}_{0}r^2\sin\theta d\phi d\theta dr$$

by a combination of sketching and substituting spherical coordinates.

After evaluating I obtain this integral to equal 3.57.

where as the first one evaluates to 5.236.

These are so difficult :(