Question:
Evaluate $\int_{-\pi}^{\pi} \frac{\cos^2 x}{1+a^x} dx$
Evaluate $\int_{-\pi}^{\pi} \frac{\cos^2 x}{1+a^x} dx$
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Even function integrals over symmetric limits simplify using doubling property.
Updated On: Jun 10, 2026
- $a\pi$
- $\frac{\pi}{a}$
- $\frac{\pi}{2}$
- $2\pi$
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The Correct Option is C
Solution and Explanation
Using symmetry:
\[
I = \int_{-\pi}^{\pi} \cos^2 x dx /2
\]
\[
I = \int_0^\pi \cos^2 x dx
\]
\[
= \int_0^\pi \frac{1+\cos 2x}{2}dx
\]
\[
= \frac{\pi}{2}
\]
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