JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\int \limits_{-\pi / 2}^{\pi / 2} \frac{1}{1+ e ^{\sin x}} d x\)
- A \(\pi\)
- B \(\frac{3 \pi}{2}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(I=\int_{-\pi / 2}^{\pi / 2} \frac{1}{1+e^{\sin x}} d x\) Apply King property \(I=\int_{E \pi / 2}^{\pi / 2} \frac{1}{1+e^{-\sin x}} d x=\int_{-\pi / 2}^{\pi / 2} \frac{e^{\sin x}}{1+e^{\sin x}} d x\)…
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