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Trigonometry — Hard JEE math MCQ

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{x^{2} \cos x}{1+e^{x}} d x$ is equal to
  1. A. $\frac{\pi^{2}}{4}-2$
  2. B. $\frac{\pi^{2}}{4}+2$
  3. C. $\pi^{2}-e^{\frac{\pi}{2}}$
  4. D. $\pi^{2}+e^{\frac{\pi}{2}}$

Solution

The correct option is **A**.

MATH

hard • PYQ Reworded
Question
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The value of ∫−π2π2x2cos⁡x1+exdx\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{x^{2} \cos x}{1+e^{x}} d x is equal to
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