MHT CET · Maths · Definite Integration
\(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{e^x(x \sin x)}{e^{2 x}-1} d x=\)
- A 0
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{2}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
\(\int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} \frac{e^x \cdot x \cdot \sin x}{e^{2 x}-1} \mathrm{~d} x=0\left[\begin{array}{c}a \\ \because \int_{-a}^a f(x) \mathrm{d} x=0 \\ \text { if } f(x) \text { is an odd function }\end{array}\right]\)
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