_ ,0 ^ ,1 d dx [ ^ - 1 ( 2x 1 + x^2 ) ] ,dx is equal to - Vidyadip

MCQ

$\int_{\,0}^{\,1} {\frac{d}{{dx}}\left[ {{{\sin }^{ - 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right)} \right]\,dx} $ is equal to

A
$0$
B
$\pi $
✓
$\pi /2$
D
$\pi /4$

✓

Answer

Correct option: C.

$\pi /2$

c
(c)$I = \left[ {{{\sin }^{ - 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right)} \right]_0^1 = {\sin ^{ - 1}}(1) - {\sin ^{ - 1}}(0)$$ = \frac{\pi }{2}$.

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