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