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Jee Main 2025 — Medium JEE math MCQ

If \( I = \int_{0}^{\pi} \frac{\sin \frac{x}{2}}{\sin \frac{x}{2} \cos \frac{x}{2}} \, dx \), then \[ I = \int_{0}^{21} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x} \, dx \] equals
  1. A. \( \frac{x^2}{12} \)
  2. B. \( \frac{x^2}{4} \)
  3. C. \( \frac{x^2}{16} \)
  4. D. \( \frac{x^2}{8} \)

Solution

The correct option is **C**. (C. \( \frac{x^2}{16} \))

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
If I=∫0πsin⁡x2sin⁡x2cos⁡x2 dx I = \int_{0}^{\pi} \frac{\sin \frac{x}{2}}{\sin \frac{x}{2} \cos \frac{x}{2}} \, dx , then I=∫021xsin⁡xcos⁡xsin⁡4x+cos⁡4x dx I = \int_{0}^{21} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x} \, dx equals
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