Question

Find the value of $n$ such that $\underset{-2}{\overset{2}{\int }}{x}^{n}dx=0.$

Answer 1

We've, $\underset{-2}{\overset{2}{\int }}f\left(x\right)dx=0$ for $f\left(x\right)$ being odd function.

Now $x^n$ will be an odd function for $n$ being odd integral value.

So, if $n$ is odd integer number then $\underset{-2}{\overset{2}{\int }}{x}^{n}dx=0$ will hold.