Average Value

Definition: Average Value of a Function Formula

Given a continuous function, $f\left(x\right)$,  the average y-value , $f_{\mathit{avg}}$, of that equation over a given closed x-interval , [ a , b ], can be found by using this equation.

$f_{\mathit{avg}}=\frac{1}{b–a}\bullet \underset{a}{\overset{b}{\int }}f\left(x\right) \mathit{dx}$

What it means:

The formula, $\frac{1}{b–a}\bullet \underset{a}{\overset{b}{\int }}f\left(x\right) \mathit{dx}$, provides you the average y-value of your given equation, $f\left(x\right)$over a given x-interval , [ a , b ].

Remember the antiderivative is a tool, and this is just one of the cool things someone found you could do with that tool.