JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\int_{-\pi / 2}^{\pi / 2} \frac{\cos ^{2} x}{1+3^{x}} d x\) is
- A \(\frac{\pi}{4}\)
- B \(4 \pi\)
- C \(\frac{\pi}{2}\)
- D \(2 \pi\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(I =\int_{-\pi / 2}^{\pi / 2} \frac{\cos ^{2} x }{1+3^{ x }} dx\) (using king) \(I =\int_{-\pi / 2}^{\pi / 2} \frac{\cos ^{2} x }{1+3^{- x }} dx =\int_{-\pi / 2}^{\pi / 2} \frac{3^{ x } \cos ^{2} x }{1+3^{ x }} dx\)…
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