Question Number 33333 by prof Abdo imad last updated on 14/Apr/18
$${let}\:{hive}\:\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\left({sinx}\right)^{{n}} \:{dx} \\ $$$${prove}\:{that}\:\:{I}_{{n}} \:\sim\:\:\sqrt{\frac{\pi}{\mathrm{2}{n}}}\:\left({n}\rightarrow\infty\right) \\ $$$$ \\ $$