MCQ
$\int_{\,\pi /6}^{\,\pi /3} {\,\frac{{dx}}{{1 + \sqrt {\cot x} }}} =$
- A$\pi /3$
- B$\pi /6$
- ✓$\pi /12$
- D$\pi /2$
$I = \int_{\pi /6}^{\pi /3} {\frac{{\sqrt {\cos x} }}{{\sqrt {\cos x} + \sqrt {\sin x} }}\,} dx$ .....(ii)
Adding (i) and (ii),
$2I = \int_{\,\pi /6}^{\,\pi /3} {dx} $;
$I = \frac{1}{2}\left( {\frac{\pi }{3} - \frac{\pi }{6}} \right) = \frac{\pi }{{12}}$.
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