Math 152 Class Notes
September 22, 2015
7.5 Average Value of a Function
Let f (x) be a function on the interval [a, b]. Then the average value of f (x) from
x = a to x = b is dened by
fave
1
=
b−a
ˆ
b
f (x)dx
a
This generalizes the concept of the average value of nitely many numbers.
Example 1. Find the average value of the function f (x) = 1 + x2 on the interval
[−1, 2].
Example 2. The normal
on a certain day in College Station is modeled
πtemperature
t , where t is the number of hours since 9 am. Find the
by T (t) = 80 + 10 sin
12
average temperature from 9 am to noon.
Example 3. Consider the function f (x) =
1
. Find the value of c such that f (c) = fave .
x2