MCQ
$\mathop \smallint \limits_0^\pi \left[ {\cot x} \right]dx = $
- A$1$
- B$-1$
- C$ - \frac{\pi }{2}$
- D$\;\frac{\pi }{2}$
$I = \int\limits_0^\pi {\left[ {\cot \left( {\pi - x} \right)} \right]} dx$
$ = \int\limits_0^\pi {\left[ { - \cot x} \right]} dx$
Adding we have
$2I = \int\limits_0^\pi {\left\{ {\left[ {\cot x} \right] + \left[ { - \cot x} \right]} \right\}} dx$
$2I = \int\limits_0^\pi {\left( { - 1} \right)} dx = - \pi $
$\therefore I = - \pi /2$
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