MA101: Single-Variable Calculus I

8.6: Average Value of Functions

• You probably learned about averages (or mean values) quite some time ago. When you have a finite number of numerical values, you add them together and divide by the number of values you have added. There is nothing preventing us from seeking the average of an infinite number of values (i.e. a function over a given interval). In fact, the formula is intuitive: we add the numbers using an integral and divide by the length of the interval.
  

• University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 6: Applications of the Integral, Section 6.5: Averages" URL

  Read Section 6.5 (pages 336-340).
  

• Massachusetts Institute of Technology: David Jerison's "Work, Average Value, Probability" Page

  Watch this video until 30:00. In this lecture, Jerison will explain how to calculate average values and weighted average values.
  

• Temple University: Gerardo Mendoza and Dan Reich's "Calculus on the Web" URL

  Click on the "Index" for Book II. Scroll down to "4. Assorted Application," and click button 124 (Average Value). Work on problems 3-11. If at any time a problem set seems too easy for you, feel free to move on.