Chapter 5.7, Problem 401E

Show that ${\displaystyle \underset{R}{\int }f\left(\sqrt{16x^2+4y+x^2}\right)dv=\frac{\pi }{2}{\displaystyle \underset{0}{\overset{1}{\int }}f\left(\rho \right){\rho }^{2}dp}}$. where f is a continuous function on 10, 11 and R is the region bounded by the ellipsoid $16x^2+4y^2+z^2=1$ .