Chapter 13.5, Problem 42E

Integrals in spherical coordinates Evaluate the following integrals in spherical coordinates.

42.     ${\displaystyle {\int }_0^{2\pi }{\displaystyle {\int }_0^{\pi /3}{\displaystyle {\int }_0^{4\sec \phi }{\rho }^2\sin \phi d\rho d\phi d\theta }}}$