0-pi-2-sin-x-cos-x-dx-

Question Number 132798 by metamorfose last updated on 16/Feb/21

{\int^{\frac{π}{2}}}_{0} (\sqrt{\sin (x)} + \sqrt{\cos (x)}) d x

Answered by Ñï= last updated on 17/Feb/21

\int_{0}^{\frac{π}{2}} (\sqrt{s i n x} + \sqrt{c o s x}) d x

= B (\frac{3}{4}, \frac{1}{2})

= \frac{Γ (\frac{3}{4}) Γ (\frac{1}{2})}{Γ (\frac{5}{4})}

= 4 \sqrt{π} \frac{Γ (\frac{3}{4})}{Γ (\frac{1}{4})}

Answered by Dwaipayan Shikari last updated on 16/Feb/21

\int_{0}^{\frac{π}{2}} \sqrt{s i n (x)} + \sqrt{c o s (x)} d x

= \frac{Γ (\frac{3}{4}) Γ (\frac{1}{2})}{Γ (\frac{5}{4})} = \frac{4 \sqrt{2} π}{Γ^{2} (\frac{1}{4})}