_0^ /2 , , x ,dx = - Vidyadip

MCQ

$\int_0^{\pi /2} {\,\,\log \tan x\,dx = } $

A
$\frac{\pi }{2}{\log _e}2$
B
$ - \frac{\pi }{2}{\log _e}2$
C
$\pi {\log _e}2$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
(d) $\int_0^{\pi /2} {\log \tan x\,dx = } \int_0^{\pi /2} {\log \left( {\frac{{\sin x}}{{\cos x}}} \right)dx} $

$ = \int_0^{\pi /2} {\log \sin x\,dx - \int_0^{\pi /2} {\log \cos x\,dx = 0} } $,

$\left\{ \because \int_{0}^{a}{f(x)dx=\int_{0}^{a}{f(a-x)dx}} \right\}$.

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