Chapter A, Problem 42E

To determine

The solution of the integral ${\displaystyle {\int }_0^{\frac{\pi }{2}}{\sin }^7\theta }d\theta$ using the result of the equation ${\displaystyle \underset{0}{\overset{\pi /2}{\int }}{\sin }^m\theta {\cos }^n\theta d\theta =}\frac{\Gamma \left(\frac{m+1}{2}\right)\Gamma \left(\frac{n+1}{2}\right)}{2\Gamma \left(\frac{m+n+2}{2}\right)}$ if $m>-1,n>-1$.