I have a question:

Suppose f is continuous and even on [−a,a], a>0 then prove that

a∫−af(x)1+exdx=a∫0f(x)dxHow can I do this? Don’t know how to start.

**Answer**

You have

I=a∫−af(x)1+ex dx⋯(1) I=a∫−af(x)1+e−x dx[∵

\textbf{Note.} A similar problem, which uses result (2) can be found here:

**Attribution***Source : Link , Question Author : James , Answer Author : Larry*