Q229 / 270 · NDA 2012 (Phase 2) · Mathematics

What is $\int_0^{\pi / 2} \sin 2 x \ln (\cot x) d x$ equal to?

  • Correct answer
    A
    0
  • B
    $\pi \ln 2$
  • C
    $-\pi \ln 2$
  • D
    $\frac{\pi \ln 2}{2}$

Solution

$\mathrm{I}=\int_0^{\pi / 2} \sin 2 x \cdot \ln (\cot x) d x$ equal to? $\because f\left(\frac{\pi}{2}-x\right)=-f(x)$ $\left\{\int_0^{2 a} f(x) d x=0\right.$, if $\left.f(2 a-x)=-f(x)\right\}$ $\therefore \quad \mathrm{I}=0$.

Hence, the correct answer is option: 'A'.

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