The value of $\int_{-\pi}^\pi \frac{\cos ^2 x}{1+a^x} d x, a>0$, is

The value of $\int_{-\pi}^\pi \frac{\cos ^2 x}{1+a^x} d x, a>0$, is
  1. $a \pi$
  2. $\frac{\pi}{2}$
  3. $\frac{\pi}{a}$
  4. $2 \pi$

Solution

$ \int_{-\pi}^\pi \frac{\cos ^2 x}{1+a^x} d x=\int_0^\pi \cos ^2 x d x=\frac{\pi}{2} . $

Asked in: JEE Main 2005

Practice more Definite Integration questions on Aicharya