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Indefinite Integrals question

2022 · 26 Jun · Shift 2 · Q31

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JEE Main
Mathematics
Indefinite Integrals
2022 · 26 Jun · Shift 2 · Q31

Indefinite Integrals question

2022 · 26 Jun · Shift 2 · Q31

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

If

\int {{1 \over x}\sqrt {{{1 - x} \over {1 + x}}} dx = g(x) + c}

,

g(1) = 0

, then

g\left( {{1 \over 2}} \right)

is equal to :

A
${\log _e}\left( {{{\sqrt 3 - 1} \over {\sqrt 3 + 1}}} \right) + {\pi \over 3}$
B
${\log _e}\left( {{{\sqrt 3 + 1} \over {\sqrt 3 - 1}}} \right) + {\pi \over 3}$
C
${\log _e}\left( {{{\sqrt 3 + 1} \over {\sqrt 3 - 1}}} \right) - {\pi \over 3}$
D
${1 \over 2}{\log _e}\left( {{{\sqrt 3 - 1} \over {\sqrt 3 + 1}}} \right) - {\pi \over 6}$

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