# Definite Integral

#### jacks

##### Well-known member
$\displaystyle \int_{0}^{\frac{\pi}{2}}\sqrt{\sin x}dx.\int_{0}^{\frac{\pi}{2}}\frac{1}{\sqrt{\sin x}}dx =$

#### JJacquelin

##### New member
Knowing the basic properties of the functions Beta and Gamma, it is easy to obtain :
first integral = (1/2)*Beta(3/4 ; 1/2)
second integral = (1/2)*Beta(1/4 ; 1/2)
and the product of the integrals = pi.