JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of the definite integral \(\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{\left(1+e^{x \cos x}\right)\left(\sin ^{4} x+\cos ^{4} x\right)}\) is equal to:
- A \(\frac{\pi}{\sqrt{2}}\)
- B \(-\frac{\pi}{4}\)
- C \(\frac{\pi}{2 \sqrt{2}}\)
- D \(-\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{2 \sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\(I=\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{d x}{\left(1+e^{x \cos x}\right)\left(\sin ^{4} x+\cos ^{4} x\right)} \cdots(1)\) Using \(\int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+b-x) d x\)…
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