Chapter 16.5, Problem 65E

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.

65. ${\displaystyle {\int }_0^{2\pi }{\displaystyle {\int }_{\pi /6}^{\pi /2}{\displaystyle {\int }_{\csc \phi }^{2}g(\rho ,\phi ,\theta ){\rho }^2}}}$ sin φ dρ dφ dθ in the orders dρ dθ dφ and dθ dρ dφ