Question

If $f\left(x\right)={\int }_0^x\frac{t^2}{e^t+e^{-t}}dt$

then $f\left(x\right)$ is?

• A. even
• B. odd
• C. periodic
• D. none of these

Answer 1

The correct option is B odd

$f\left(x\right)={\int }_0^x\frac{t^2}{e^t+e^{-t}}dt$
$f^{\prime }\left(x\right)=\frac{t^2}{e^t+e^{-t}}=f^{\prime }(-x)$
Clearly $f^{\prime }\left(x\right)$ is an even function.
Hence $f\left(x\right)$ will be an odd function.