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Multiple Choice: The average value of on the interval is closest to:

You are given and you want to find the average (mean) value of . Will you integrate and divide, or will you find the slope of the secant line?

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