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