JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\int \limits_{0}^{\pi} \frac{e^{\cos x} \sin x}{\left(1+\cos ^{2} x\right)\left(e^{\cos x}+e^{-\cos x}\right)} d x\) is equal to
- A \(\frac{\pi^{2}}{4}\)
- B \(\frac{\pi^{2}}{2}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\int \limits_{0}^{\pi} \frac{e^{\cos x} \sin x}{\left(1+\cos ^{2} x\right)\left(e^{\cos x}+e^{-\cos x}\right)} d x\) Use King's property \(I=\int \limits_{0}^{\pi} \frac{e^{-\cos x} \sin x}{\left(1+\cos ^{2} x\right)\left(e^{-\cos x}+e^{\cos x}\right)} d x\) On adding equation…
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