Chapter 4: Integration
Section 4.6: Average Value and the Mean Value Theorem
In the interval 0,π, find all values of c for which fc=favg.
From Example 4.6.2, favg=2/π. Hence, the equation sinc=2/π must be solved for c. Figure 4.6.2(a) and Figure 4.6.2(b), and the appropriate calculations, show that c1=arcsin2/π≐0.69011, and c2=π−arcsin2/π≐2.4515.
Tools≻Load Package: Student Calculus 1
Find all solutions
Write the equation fc=favg; press the Enter key.
Context Panel: Student Calculus1≻Solve≻Find Roots
See Figure 4.6.3(a) for Roots dialog.
For exact roots, uncheck "calculate numerically"
For numeric roots, ckeck "calculate numerically"
Figure 4.6.3(a) Roots dialog
Alternatively, apply the Roots command directly
Apply the Roots command in the Student Calculus1 package. In this form, exact solutions are returned, if possible.
Apply the Roots command in the Student Calculus1 package. In this form, numeric solutions are returned.
The Roots command, which attempts to return all real solutions (of an equation) in a bounded interval, is not presently available in the Context Panel's Solve options prior to Maple 18. The closest syntax-free access to the command in these earlier versions of Maple is via the task template shown in Table 4.6.3(a).
Tools≻Tasks≻Browse: Algebra≻Solve Analytically in Specified Interval
Solve Analytically in a Specified Interval
Enter an expression:
Find the roots in a specified interval:
Express the roots in floating-point form:
Table 4.6.3(a) Roots command implemented via task template
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