_ - 1 2 ^ ,1 2 x , 1 + x 1 - x dx is equal to - Vidyadip

MCQ

$\int_{ - \frac{1}{2}}^{\,\frac{1}{2}} {\cos x\,\ln \frac{{1 + x}}{{1 - x}}dx} $ is equal to

✓
$0$
B
$1$
C
$2$
D
$ln \, 3$

✓

Answer

Correct option: A.

$0$

a
(a) $I = \int_{ - 1/2}^{1/2} {\cos x\ln \left( {\frac{{1 + x}}{{1 - x}}} \right)\,dx} $

$\cos x\ln \left( {\frac{{1 + x}}{{1 - x}}} \right)$ is an odd function, $ \because f( - x) = - f(x)$)

$\therefore$ $I = 0$.

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