JEE Main 2024 Mathematics question
is equal to .
Answer: 15
Solution
Let I = ∫₀^π x² sin x cos x/(sin⁴x + cos⁴x)dx. Replacing x by π − x (sin x cos x changes sign) and adding: 2I = ∫₀^π[x² − (π − x)²] sin x cos x/(sin⁴x + cos⁴x)dx = π∫₀^π(2x − π) sin x cos x/(sin⁴x + cos⁴x)dx. The integrand is symmetric about x =
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