$\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{e^x(x \sin x)}{e^{2 x}-1} d x=$

$\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{e^x(x \sin x)}{e^{2 x}-1} d x=$
  1. 0
  2. $\frac{\pi}{3}$
  3. $\frac{\pi}{2}$
  4. $\frac{\pi}{4}$

Solution

$\int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} \frac{e^x \cdot x \cdot \sin x}{e^{2 x}-1} \mathrm{~d} x=0\left[\begin{array}{c}a \\ \because \int_{-a}^a f(x) \mathrm{d} x=0 \\ \text { if } f(x) \text { is an odd function }\end{array}\right]$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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