#### Average Value of a Function

- The average value of a function f(x) for an interval [a,b]

is defined as:

\text { Average Value }=\frac{1}{b-a} \int_{a}^{b} f(x) d x

- Graphically, it is equivalent as drawing a rectangle that has length b-a, and has an area that equals \int_{a}^{b} f(x) d x, or the area under the curve for the interval [a,b]. Therefore, the height of this rectangle is the average value of f(x)