_ - 1 ^1 2 - x 2 + x ,dx = - Vidyadip

MCQ

$\int_{ - 1}^1 {\log \frac{{2 - x}}{{2 + x}}\,dx} = $

A
$2$
B
$1$
C
$ - 1$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
(d) Let $f(x) = \log \left( {\frac{{2 - x}}{{2 + x}}} \right)$

$ \Rightarrow f( - x) = \log {\left( {\frac{{2 - x}}{{2 + x}}} \right)^{ - 1}} $

$= - \log \left( {\frac{{2 - x}}{{2 + x}}} \right) = - f(x)$

$\therefore $ $\int_{ - 1}^1 {\log \left( {\frac{{2 - x}}{{2 + x}}} \right)\,\,dx = 0} $.

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