Question:
The value of $\int_{-\pi / 2}^{\% / 2} \frac{\cos ^{2} x}{1+3^{x}} d x$ is:
Correct Option: , 4
Solution:
Let $I=\int_{-\pi / 2}^{5 / 2} \frac{\cos ^{2} x}{1+3^{x}} d x$
$I=\int_{-\pi / 2}^{\pi / 2} \frac{3^{x} \cos ^{2} x}{1+3^{x}} d x$
$2 I=\int_{-\pi / 2}^{/ 2} \cos ^{2} x d x$
$I=\int_{0}^{\pi / 2} \cos ^{2} x d x=\frac{\pi}{4}$
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