_0^ 3 , ,1 2 , ,d dx , ( ^ - 1 2x 1 - x^2 )dx equals - Vidyadip

MCQ

$\int\limits_0^{\sqrt 3 } {\,\,\frac{1}{2}\,} \,\frac{d}{{dx}}\,\left( {{{\tan }^{ - 1}}\frac{{2x}}{{1 - {x^2}}}} \right)dx$ equals

✓
$\frac{\pi }{3}\,$
B
$ - \,\,\frac{\pi }{6}\,$
C
$\,\frac{\pi }{2}\,$
D
$\,\frac{\pi }{4}\,$

✓

Answer

Correct option: A.

$\frac{\pi }{3}\,$

a
$ta{n^{ - 1}}\left( {\frac{{2x}}{{1 - {x^2}}}} \right)=$$\left[ {\begin{array}{*{20}{c}}
{2{{\tan }^{ - 1}}x\,\,\,\,\,\,\,\,\,if{\mkern 1mu} {\mkern 1mu} 0 < x < 1} \\
{2{{\tan }^{ - 1}}x - \pi \,\,\,\,\,if{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} x > 1}
\end{array}} \right.$

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