Average Value 

Copyright Maplesoft, a division of Waterloo Maple Inc., 2007 

Introduction 

This application is one of a collection of examples teaching Calculus with Maple. These applications use Clickable Calculus? methods to solve problems interactively. Steps are given at every stage of the solution, and many are illustrated using short video clips.  Click on the buttons to watch the videos. 

Problem Statement 

Obtain the average value of , . 

 

Solution 

Two methods can be used to solve the problem. The first method makes use of the function averaging tutor and the second method computes the average value of the function from first principles. 

Method 1 

 

Step	Result
Load the Student Calculus 1 package.    This can be done by executing   with(Student[Calculus1]), or by clicking Tools>Load Package>Student Calculus 1.	Loading Student:-Calculus1
Enter the expression for the function.      Launch and use the Function Average tutor.    Right-click on the expression for the function.  Select  Tutors>Calculus - Single Variable>Function Average. Adjust the a and b values to -1 and 6 to match the range. Click Display to update the plot and function average. See Figure 1 below.	(3.1.1)
Figure 2 The Function Average tutor applied to

Method 2 

The average value of on is . 

 

Step	Result
Enter the expression for the function and press [Enter].	(3.2.1)
Enter the expression for the average value.     Use the Expression palette and to define the average value expression. Reference the function by its equation label. Press [Enter] evaluate the integral  .	(3.2.2)
Plot the function and the average value on one set of axes.    On a new line enter the label references for the function and the average value  ([Ctrl+L] then the label number) seperated by a comma. [Enter]. Right-click, Plots>Plot Builder. Set and .	(3.2.3)

Legal Notice: The copyright for this application is owned by Maplesoft. The application is intended to demonstrate the use of Maple to solve a particular problem. It has been made available for product evaluation purposes only and may not be used in any other context without the express permission of Maplesoft.