_ /6 ^ /4 cosec ,2x ,dx = - Vidyadip

MCQ

$\int_{\pi /6}^{\pi /4} {{\rm{cosec}}\,2x\,dx = } $

A
$\log 3$
B
$\log \sqrt 3 $
C
$\log 9$
✓
$\frac{1}{2}\log \sqrt 3 $

✓

Answer

Correct option: D.

$\frac{1}{2}\log \sqrt 3 $

d
(d) $\int_{\pi /6}^{\pi /4} {{\rm{cosec}}\,2x\,dx} = \frac{1}{2}[\log \tan x]_{\pi /6}^{\pi /4}$

$ = \frac{1}{2}\left[ {\log \tan \frac{\pi }{4} - \log \tan \frac{\pi }{6}} \right] = \frac{1}{2}\log \sqrt 3 $.

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