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