Average Function

If $f$ is Continuous on a Closed Interval $[a,b]$, then there is at least one number $x^*$ in $[a,b]$ such that

$$\int_a^b f(x)dx = f(x^*)(b-a).$$

The average value of the Function $({\overline f})$ on this interval is then given by $f(x^*)$.

See Mean-Value Theorem