question_answer

The value of \[\int_{-\pi }^{\pi }{\frac{{{\cos }^{2}}x}{1+{{a}^{x}}}}dx,a>0,\]is     AIEEE  Solved  Paper-2005

A) \[2\pi \]               

B)        \[\frac{\pi }{a}\]                              

C)        \[\frac{\pi }{2}\]              

D)        \[a\pi \]

Correct Answer: C

Solution :

Let               ?..(i)                                 ?..(ii) On adding Eqs. (i) and (ii), we get                                                              \[l=\frac{\pi }{2}\]