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Definite Integration question

2025 · 23 Jan · Shift 2 · Q26

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PYQ Library
JEE Main
Mathematics
Definite Integration
2025 · 23 Jan · Shift 2 · Q26

Definite Integration question

2025 · 23 Jan · Shift 2 · Q26

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

If

\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

\int_0^{2I} \frac{x \sin x \cos x}{\sin ^4 x+\cos ^4 x} \mathrm{~d} x

equals :

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

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