Average value of a function

The  exercise appears under the Integral calculus Math Mission. This exercise plays with the average value of a function and applications.

Types of Problems
There are three types of problems in this exercise:


 * 1) Find the average value of the function: This problem provides a function and an interval. The student is asked to find the average value of the function over the interval.Avoaf1.png
 * 2) Use average value to find the constant: This problem provides a function and interval involving a constant, and the average value. The student is expected to work backwards to find the value of the missing constant.Avoaf2.png
 * 3) Find the height of the right rectangle: This problem has the graph of a function. The student is asked to find the appropriate height of a rectangle that could be used to represent the exact area under the curve over the interval.Avoaf3.png

Strategies
Knowledge of average/mean and basic integration ability are encouraged to ensure success on this exercise.
 * 1) The average value of a function is the integral over an interval, divided by the length of the interval.
 * 2) Average value of a function is the arithmetic mean extended to a continuous case.
 * 3) The average value of a function can be connected with the FTC.

Real-life Applications

 * 1) Average has the same applications as mean does in statistics, it can be thought of as a typical value.
 * 2) Some of the problems in this exercise are applications.