When finding the [[Average]] of a [[Discrete]] set, you take the sum of all elements and divide by the number of elements. $\huge \op{avg}(S) = \frac{1}{|S|} \sum^{|S|}_{i} S_{i} $ But for finding the average of a [[Function]] over a [[Continuous]] [[Interval]], you would need to find the [[Limits|limit]] of the average as you add more and more samples. To find the [[Average]] of a [[Function]] over the [[Interval]] $[a,b]$: $\huge \begin{align} \let \Delta x &= \frac{{b-a}}{N} \\ \frac{1}{b-a}\lim_{N\to \infty} \sum^N_{i=1}{ f(x_{i}^*) \Delta x } &= \frac{1}{b-a} \int_{a}^b f(x)\d{x} \end{align} $