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Question: Answered & Verified by Expert
The value of $\int_{-\pi}^\pi \frac{\cos ^2 x}{1+a^x} d x, a>0$, is
MathematicsDefinite IntegrationJEE MainJEE Main 2005
Options:
  • A
    $a \pi$
  • B
    $\frac{\pi}{2}$
  • C
    $\frac{\pi}{a}$
  • D
    $2 \pi$
Solution:
2635 Upvotes Verified Answer
The correct answer is:
$\frac{\pi}{2}$
$$
\int_{-\pi}^\pi \frac{\cos ^2 x}{1+a^x} d x=\int_0^\pi \cos ^2 x d x=\frac{\pi}{2} .
$$

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