MATH 2B Lecture Notes - Lecture 10: Riemann SumPremium
Course CodeMATH 2B
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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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