\(\displaystyle \phi = \frac { \pi }{4} \) and \(\displaystyle \phi = arctan 2 \),

and the sphere \(\displaystyle \rho = \sqrt {6} \), and has density proportional to the distance from the origin. Find the mass.

is the following correct?

\(\displaystyle

\int_{0}^{ \frac { \pi } {2} } \int_{ \frac { \pi } {4} }^{arctan(2)} \int_{0}^{ \sqrt{6} } \rho ~ \rho^2 sin \phi ~d \rho ~d \phi ~d \theta

\)