Q62 / 150 · MHT CET 2020 (14 Oct Shift 1) · Mathematics

$\int_{-\pi}^{\pi} \frac{2 x}{1+\cos ^{2} x} d x=$

  • A
    $\pi$
  • Correct answer
    B
    $0$
  • C
    $1$
  • D
    $-\pi$

Solution

Let $f(x)=\frac{2 x}{1+\cos ^{2} x} \Rightarrow f(-x)=\frac{-2 x}{1+\cos ^{2} x}$ Thus $\mathrm{f}(-\mathrm{x})=-\mathrm{f}(\mathrm{x}) \Rightarrow \mathrm{I}=0$

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

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