_0^ /2 ^5 x ,dx = - Vidyadip

MCQ

$\int_0^{\pi /2} {{{\sin }^5}x\,dx = } $

✓
$\frac{8}{{15}}$
B
$\frac{4}{{15}}$
C
$\frac{{8\sqrt \pi }}{{15}}$
D
$\frac{{8\pi }}{{15}}$

✓

Answer

Correct option: A.

$\frac{8}{{15}}$

a
(a)$\int_0^{\pi /2} {{{\sin }^5}xdx = \frac{{\Gamma (3).\Gamma (1/2)}}{{2.\Gamma (7/2)}} = \frac{8}{{15}}} $.

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