_0^ /2 ^2 x ^3 x ,dx = - Vidyadip

MCQ

$\int_0^{\pi /2} {{{\sin }^2}x{{\cos }^3}x} \,dx = $

A
$0$
✓
$\frac{2}{{15}}$
C
$\frac{4}{{15}}$
D
None of these

✓

Answer

Correct option: B.

$\frac{2}{{15}}$

b
(b) Using gamma function,

$\int_0^{\pi /2} {{{\sin }^2}x{{\cos }^3}xdx = \frac{{\Gamma \,\left( {\frac{3}{2}} \right)\,\Gamma 2}}{{2\Gamma \left( {\frac{7}{2}} \right)}} = \frac{2}{{15}}} $.

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