JEE Mains · Maths · STD 12 - 7.2 definite integral
\(\left|\frac{120}{\pi^3} \int_0^\pi \frac{x^2 \sin x \cos x}{\sin ^4 x+\cos ^4 x} d x\right|\) is equal to ...........
- A \(15\)
- B \(16\)
- C \(17\)
- D \(18\)
Answer & Solution
Correct Answer
(A) \(15\)
Step-by-step Solution
Detailed explanation
\(\int_0^\pi \frac{x^2 \sin x \cdot \cos x}{\sin ^4 x+\cos ^4 x} d x\) \(=\int_0^{\frac{\pi}{2}} \frac{\sin x \cdot \cos x}{\sin ^4 x+\cos ^4 x}\left(x^2-(\pi-x)^2\right) d x\) \(=\int_0^{\frac{\pi}{2}} \frac{\sin x \cdot \cos x\left(2 \pi x-\pi^2\right)}{\sin ^4 x+\cos ^4 x}\)…
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