AP EAMCET · Maths · Definite Integration
\(\int_0^\pi \frac{x \sin x}{1+\cos ^2 x} d x=\)
- A \(\frac{\pi^2}{4}\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi^2}{2}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi^2}{4}\)
Step-by-step Solution
Detailed explanation
\(I = \int_0^\pi \frac{x \sin x}{1+\cos^2 x} dx\) ... (1) \(I = \int_0^\pi \frac{(\pi-x) \sin(\pi-x)}{1+\cos^2(\pi-x)} dx = \int_0^\pi \frac{(\pi-x) \sin x}{1+\cos^2 x} dx\) ... (2)…
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