JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of the integral \(\int_{-\pi/4}^{\pi/4}\left(\dfrac{32\cos^4 x}{1 + e^{\sin x}}\right)dx\) is:
- A \(4\pi + 2\)
- B \(3\pi + 8\)
- C \(3\pi + 4\)
- D \(4\pi + 3\)
Answer & Solution
Correct Answer
(B) \(3\pi + 8\)
Step-by-step Solution
Detailed explanation
Let \(I = \int_{-\pi/4}^{\pi/4} \dfrac{32\cos^4 x}{1 + e^{\sin x}} dx\) Using the definite integral property \(\int_{-a}^{a} f(x) dx = \int_{0}^{a} (f(x) + f(-x)) dx\), we get:…
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