_0^ / 2 ^ 3 2 x d x ^ 3 2 x+ ^ 3 2 x = - Vidyadip

MCQ

$\int_0^{\pi / 2} \frac{\sin ^{\frac{3}{2}} x d x}{\cos ^{\frac{3}{2}} x+\sin ^{\frac{3}{2}} x}=$

A
$0$
B
$\pi$
C
$\frac{\pi}{2}$
✓
$\frac{\pi}{4}$

✓

Answer

Correct option: D.

$\frac{\pi}{4}$

(D)
$\int_0^{\frac{\pi}{2}} \frac{\sin ^{ n } x}{\sin ^{ n } x+\cos ^{ n } x} d x=\int_0^{\frac{\pi}{2}} \frac{\cos ^{ n } x}{\sin ^{ n } x+\cos ^{ n } x} d x=\frac{\pi}{4}$
$\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\cos ^{\frac{3}{2}} x+\sin ^{\frac{3}{2}} x} d x=\frac{\pi}{4} $

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