Chapter 14, Problem 66RE

To determine

To calculate: The value of provided triple integral ${\displaystyle {\int }_0^{\frac{\pi }{2}}{\displaystyle {\int }_0^{\frac{\pi }{2}}{\displaystyle {\int }_0^{\cos \varphi }{\rho }^2\cos \theta d\rho d\theta d\varphi }}}$ by the use of computer algebra system.