JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of the integral \(\int \limits_{-\pi / 2}^{\pi / 2} \frac{d x}{\left(1+e^{x}\right)\left(\sin ^{6} x+\cos ^{6} x\right)}\) is equal to
- A \(2 \pi\)
- B \(0\)
- C \(\pi\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(C) \(\pi\)
Step-by-step Solution
Detailed explanation
\(I=\int \limits_{-\pi / 2}^{0} \frac{d x}{\left(1+e^{x}\right)\left(\sin ^{6} x+\cos ^{6} x\right)}+\int \limits_{0}^{\pi / 2} \frac{d x}{\left(1+e^{x}\right)\left(\sin ^{6} x+\cos ^{6} x\right)}\) Put \(x =- t\)…
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