# Definite Integrals

# Average Value

You know how to take the average of a group of numbers: add all the numbers and divide by how many there are.

What would the "average value" of a function be?

A function like *f* (*x*) = *x* or *f* (*x*) = *e*^{x} takes on infinitely many values. We can't add infinitely many values and divide by \infty.

However, there is a reasonable way to define the average value of a function on an interval.

First we're going to briefly revisit taking averages of numbers. We want to think about averages of numbers in a specific way that will make it easier to understand what the average of a function means.