Chapter 7.4, Problem 1P

Show that if $f(x)$ has period $p$, the average value of $f$ is the same over any interval of length $p$.

Hint: Write ${\displaystyle {\int }_a^{a+p}f}(x)dx$ as the sum of two integrals ( $a$ to $p$, and $p$ to $a+p)$ and make the change of variable $x=t+p$ in the second integral.