AP EAMCET · Maths · Definite Integration
If \(\int_0^\pi \frac{x \sin x}{4 \cos ^2 x+3 \sin ^2 x} d x=\)
- A \(\frac{\pi^2}{6 \sqrt{3}}\)
- B \(\frac{\pi}{3 \sqrt{3}}\)
- C \(\frac{\pi^2}{3 \sqrt{3}}\)
- D \(\sqrt{3} \pi^2\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi^2}{6 \sqrt{3}}\)
Step-by-step Solution
Detailed explanation
\(I=\int_0^\pi \frac{x \sin x}{4 \cos ^2 x+3 \sin ^2 x} d x\) \(\Rightarrow I=\int_0^\pi \frac{x \sin x}{\cos ^2 x+3} d x\) ....(i) \(\Rightarrow I=\int_0^\pi \frac{(\pi-x) \sin x}{\cos ^2 x+3} d x\) ....(ii) Adding (i) and (ii)…
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