If I = ∫₀^(π/2) (sin^(3/2) x)/(sin^(3/2) x + cos^(3/2) x) dx, the… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 23 January, Shift 2Definite Integrals

If $I = \int_0^{\frac{\pi}{2}} \frac{\sin^{\frac{3}{2}} x}{\sin^{\frac{3}{2}} x + \cos^{\frac{3}{2}} x} \, dx,$ then $\int_0^{2I} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x} \, dx$ equals:

A
$\frac{\pi^2}{16}$
B
$\frac{\pi^2}{4}$
C
$\frac{\pi^2}{8}$
D
$\frac{\pi^2}{12}$

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