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ERJAEE, G. (20)

Lecture 10

Department

MathematicsCourse Code

MATH 2BProfessor

ERJAEE, G.Lecture

10This

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MATH 2B - Lecture 10 - Average Value of a Function

Recall the usual meaning of average: if we have a collection of n values then

its average is

Now observe that a Riemann sum for a function f on an interval [a,b] is simply the

average value of the rectangle-heights , multiplied by the length of [a,b]:

● This motivates us to define the notion of average for any integrable function.

The average value of a function f over [a,b] is:

We knew that the definite integral

is the net area bounded by f(x) on [a,b].

Reformulating the formula gives:

=

Area under function Rectangular Area

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