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Definite Integral

jacks

Well-known member
Apr 5, 2012
226
$\displaystyle \int_{0}^{\frac{\pi}{2}}\sqrt{\sin x}dx.\int_{0}^{\frac{\pi}{2}}\frac{1}{\sqrt{\sin x}}dx =$
 

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.