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If the graph at right represents distance over time between a space shuttle and Earth, how would you determine the average velocity? Describe the method you would use.

Given a distance function, will average velocity be represented by 'average area under the curve' or 'average rate of change'?

Average (Mean) Values

To calculate the mean (average) value of a finite set of items, add up the values of items and divide by the number of items.

Integrals help us add over a continuous interval. Therefore, for any continuous function :

mean value of over

Since , we can also calculate the average value of any function using its antiderivative . Its average slope gives the average rate of change of , which is the same as the average value of

  mean rate of change of over