$\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{e^x(x \sin x)}{e^{2 x}-1} d x=$
$\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{e^x(x \sin x)}{e^{2 x}-1} d x=$
- 0
- $\frac{\pi}{3}$
- $\frac{\pi}{2}$
- $\frac{\pi}{4}$
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)
Practice more Definite Integration questions on Aicharya