Chapter 5.5, Problem 273E

Show that if $F\left(\rho ,\theta ,\phi \right)=f\left(\rho \right)g\left(\theta \right)h\left(\phi \right)$ is a continuous function on the spherical box $B=\left\{\left(\rho -\theta ,\phi \right)\right\}\left[a\le \rho ,\le b,a\le \theta \le \beta ,\gamma \le \phi \le \Psi \right]$, then ${\displaystyle \underset{B}{\iiint }dfV=\left({\displaystyle \underset{a}{\overset{b}{\int }}{\rho }^{2}f\left(\rho \right)dr}\right)\left({\displaystyle \underset{a}{\overset{\beta }{\int }}g\left(\theta \right)d\theta }\right)\left({\displaystyle \underset{\gamma }{\overset{\Psi }{\int }}h\left(\phi \right)\sin \phi d\phi }\right)}$