_0^ 2 4x ,x , + , x^2 , ,x 2 ,x dx is equal to

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MCQ

$\int\limits_0^{\frac{\pi }{2}} { {\frac{{4x\sin \,x\, + \,{x^2}\,\cos \,x}}{{2\sqrt {\sin \,x} }}} dx }$ is equal to

A
$\frac{\pi}{2}$
✓
$\frac{\pi^2}{4}$
C
$\frac{\pi}{4}$
D
$\frac{\pi^2}{16}$

✓

Answer

Correct option: B.

$\frac{\pi^2}{4}$

b
$\int_{0}^{\pi / 2}\left(2 x \sqrt{\sin x}+\frac{x^{2} \cos x}{2 \sqrt{\sin x}}\right) d x$

$\int_{0}^{\pi / 2} \frac{d}{d x}\left(x^{2} \sqrt{\sin x}\right) d x=\frac{\pi^{2}}{4}$

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