# Who's up to the challenge? 71

Calculus Level 5

$\int _{ 0 }^{ \pi /2 }{ \sqrt { \sin { x } } \, dx } =\dfrac { \sqrt { A } }{ \sqrt { \pi } } \left(\Gamma \left( \frac { C }{ D } \right)\right)^B$

The equation above holds for positive integers $$A,B,C$$ and $$D$$ with $$C,D$$ coprime. Find $$A+B+C+D$$.

Notation: $$\Gamma(\cdot)$$ denotes the Gamma function.

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