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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_0^{\pi /2} {x\cot x\,dx} $ equals
  • A
    $ - \frac{\pi }{2}\log 2$
  • ✓
    $\frac{\pi }{2}\log 2$
  • C
    $\pi \log 2$
  • D
    $ - \pi \log 2$
✓

Answer

Correct option: B.
$\frac{\pi }{2}\log 2$
b
(b) $I = \int_0^{\pi /2} {x\cot x\,dx} $

Integrating by parts, we get 

$[x(\log \sin x)]_0^{\pi /2} - \int_0^{\pi /2} {\log \sin x\,dx} $

$I = - \left( { - \frac{\pi }{2}\log 2} \right) = \frac{\pi }{2}\log 2$.

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