Definite Integration JEE Main 2025 | Evaluate Given Integral

JEE MAIN 2025

23-01-2025 SHIFT-2

Question

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 $\int_{0}^{21} \frac{x \sin x \cos x}{\sin ^{4} x+\cos ^{4} x} \mathrm{~d} x$ equals :

Select the correct option:

$\frac{\pi^{2}}{16}$

$\frac{\pi^{2}}{12}$

$\frac{\pi^{2}}{4}$

$\frac{\pi^{2}}{8}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Medium

Start Preparing for JEE with Competishun

Report Issue