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STD 12 - 7.2 definite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.2 definite integral4 Marks
MCQ
$\mathop \smallint \limits_0^\pi \left[ {\cot x} \right]dx = $
  • A
    $1$
  • B
    $-1$
  • ✓
    $ - \frac{\pi }{2}$
  • D
    $\;\frac{\pi }{2}$
✓

Answer

Correct option: C.
$ - \frac{\pi }{2}$
c
$I = \int\limits_0^\pi  {\left[ {\cot x} \right]} dx$

$I = \int\limits_0^\pi  {\left[ {\cot \left( {\pi  - x} \right)} \right]} dx$

$ = \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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