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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.