Average Value via Integrals

The average value of an integrable function on an interval can be defined using integrals: , or, equivalently, , so, for positive functions, the average value is the height of the rectangle with width that has the same area as the region betwen the graph and the interval on the axis. This Demonstration illustrates that fact.

SNAPSHOTS

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DETAILS

When "show rectangle" is checked, notice that the blue area is the same as the red area.
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