Chapter 4: Integration
Section 4.6: Average Value and the Mean Value Theorem
Example 4.6.2
Obtain the average value of on the interval .
Solution
Mathematical Solution
The average value, computed as per Definition 4.6.1, is
Figure 4.6.2(a) Average value for on
Figure 4.6.2(a) is a graphical representation of the average value for on the interval .
Maple Solutions
Solution by tutor
Figure 4.6.2(b) shows the result of applying the tutor to on . The graph is drawn, the average value calculated, and a dotted line corresponding to the average value is appended to the graph.
The tutor gives simplified access to the FunctionAverage command, which will return either the average value, or a figure comparable to Figure 4.6.1(a).
The Maple command at the bottom of the tutor shows the syntax that generates the graph provided by the tutor.
Figure 4.6.2(b) Function Average tutor
Solution from first principles
Write as a multiplier of Calculus palette: Definite Integral template
Context Panel: Evaluate and Display Inline
=
Table 4.6.2(a) details the use of the FunctionAverage command.
Tools≻Load Package: Student Calculus 1
Loading Student:-Calculus1
Table 4.6.2(a) Direct use of the FunctionAverage command
The option is also valid, and leads to a graph similar to the one shown in Figure 4.6.2(b). If in addition the option is included, the graph will resemble the one in Figure 4.6.2(a).
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