let-hive-I-n-0-pi-2-sinx-n-dx-prove-that-I-n-pi-2n-n-

Question Number 33333 by prof Abdo imad last updated on 14/Apr/18

l e t h i v e I_{n} = \int_{0}^{\frac{π}{2}} {(s i n x)}^{n} d x

p r o v e t h a t I_{n} \sim \sqrt{\frac{π}{2 n}} (n \to \infty)