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Average Function Value
The first application of integrals that we’ll take a look at is the average value of a
function. The following fact tells us how to compute this.
Average Function Value
The average value of a function
over the interval [
a,b
] is given by,
To see a justification of this formula see the
Proof of Various Integral
Properties
section of the Extras chapter.
Let’s work a couple of quick examples.
Example 1
Determine the average value of each of the following functions on the given interval.
(a)
on
[
Solution
]
(b)
o
n
[
Solution
]
Solution
(a)
o
n
There’s really not a whole lot to do in this problem other than just use the formula.
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So, the average value of this function of the given interval is 1.620993.
[
Return to Problems
]
(b)
o
n
Again, not much to do here other than use the formula. Note that the integral will need the
following substitution.
Here is the average value of this function,
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This note was uploaded on 11/06/2011 for the course MATH 151 taught by Professor Sc during the Fall '08 term at Rutgers.
 Fall '08
 sc
 Integrals

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