Chapter 16.5, Problem 64E

Changing order of integration if possible, write iterated integrals in spherical coordinates for the following regions in the specified orders. Sketch the region of integration. Assume g is continuous on the region.

64. ${\displaystyle {\int }_0^{2\pi }{\displaystyle {\int }_0^{\pi /2}{\displaystyle {\int }_0^{4\sec \phi }g(\rho ,\phi ,\theta ){\rho }^2}}}$ sin φ dρ dφ dθ in the orders dρ dθ dφ and dθ dρ dφ