MHT CET · Maths · Definite Integration
\(\int_{-\pi}^{\pi} \frac{2 x}{1+\cos ^{2} x} d x=\)
- A \(\pi\)
- B \(0\)
- C \(1\)
- D \(-\pi\)
Answer & Solution
Correct Answer
(B) \(0\)
Step-by-step Solution
Detailed explanation
Let \(f(x)=\frac{2 x}{1+\cos ^{2} x} \Rightarrow f(-x)=\frac{-2 x}{1+\cos ^{2} x}\)
Thus \(\mathrm{f}(-\mathrm{x})=-\mathrm{f}(\mathrm{x}) \Rightarrow \mathrm{I}=0\)
Thus \(\mathrm{f}(-\mathrm{x})=-\mathrm{f}(\mathrm{x}) \Rightarrow \mathrm{I}=0\)
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