TS EAMCET · Maths · Definite Integration
\(\int_0^{\pi / 2} \frac{\pi \sin x}{1+\cos ^2 x} d x\) is equal to
- A \(\pi^2\)
- B \(\frac{\pi^2}{2}\)
- C \(\frac{\pi^2}{4}\)
- D \(\frac{\pi^2}{6}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi^2}{4}\)
Step-by-step Solution
Detailed explanation
Let \(I=\int_0^{\pi / 2} \frac{\pi \sin x}{1+\cos ^2 x} d x\) Put \(\cos x=t \Rightarrow-\sin x d x=d t\)…
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