This preview shows pages 1–3. Sign up to view the full content.
Thursday, November 17
−
Lecture 28 :
Average value of a function.
(Refers to
Section 7.7 your text)
Students who have mastered the content of this lecture know
:
About the average value of a function
over an interval [a, b], the mean value theorem for integrals.
Students who have practiced the techniques presented in this lecture will be able to
:
Compute the
average value of a function over an interval [a, b], state the Mean value theorem for integrals.
28.1
Average value of f(x)
−
Let
f
(
x
) be a continuous function over the interval [
a
,
b
].
We recognize the expression
as being a Riemann sum where the interval is partitioned into
n
equal subintervals each of
length
∆
x
= (
b
–
a
)/
n
. The
x
i
*
can be chosen to be the right endpoint of the each
subinterval. For a particular value of
n
we also recognize the expression
as being an
average
of
n
chosen values of
f
over
[
a, b
].
Then we can write
Given that
we define the
average value of a function f(x) over an interval [a, b]
as
Note the authors of your text use the notation:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document28.1.1
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 RobertAndre
 Calculus, Mean Value Theorem

Click to edit the document details