6'5 Average Value of a Function

1
6.5 Average Value of a Function
If f is continuous on a, b, then the average
value of f on this interval is given by
2
Mean Value Theorem for Integrals
If f is continuous on a, b, then there exists a
number c in a, b such that
y
Note The area under f is equal to the area of
the rectangle whose height is the average value.
x
a
c
b
3
Example 1
Find the average value of the function on the
given interval.
Solution
4
Example 2

• Find the average value of f on the given
  interval.
• Find c such that
• Sketch the graph of f and a rectangle whose area
  is the same as the area under the graph of f .

y
Solution
4
x
1
1 c
2