Chapter 11.7, Problem 7P

Express the following integrals as $B$ functions, and then, by $(7.1),$ in terms of $\Gamma$ functions. When possible, use $\Gamma$ function formulas to write an exact answer in terms of $\pi ,\sqrt{2},$ etc.

Compare your answers with computer results and reconcile any discrepancies.

${\displaystyle {\int }_0^{\pi /2}\frac{d\theta }{\sqrt{\sin \theta }}}$