Nov 20, 2012 Thread starter #1 J jacks Well-known member Apr 5, 2012 226 $\displaystyle \int_{0}^{\frac{\pi}{2}}\sqrt{\sin x}dx.\int_{0}^{\frac{\pi}{2}}\frac{1}{\sqrt{\sin x}}dx =$

$\displaystyle \int_{0}^{\frac{\pi}{2}}\sqrt{\sin x}dx.\int_{0}^{\frac{\pi}{2}}\frac{1}{\sqrt{\sin x}}dx =$

Nov 20, 2012 #2 J JJacquelin New member Jul 31, 2012 3 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.

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.