Mathematics · 2025
JEE Main · 23 January 2025, Shift 2 · Q18
If I =∫_0^((π)/2) (sin^(3/2) x)/(sin^(3/2) x+ cos^(3/2) x) d x, then ∫_0^2 I (x sin x cos x)/(sin^4 x+ cos^4 x) d x equals:
If $\displaystyle \mathrm{I}=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} \mathrm{~d} x$, then $\displaystyle \int_0^{2 \mathrm{I}} \frac{x \sin x \cos x}{\sin ^4 x+\cos ^4 x} \mathrm{~d} x$ equals :
Official answer
From NTA’s final answer key for this paper.
(4)
$\displaystyle \frac{\pi^2}{16}$
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JEE Main 2025 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.