Because the triple integral over can be iterated in cylindrical coordinates in the order , the task template in Table 8.2.11(a), implementing the FunctionAverage command from the Student MultivariateCalculus package, can be used.
Tools≻Tasks≻Browse:
Calculus - Multivariate≻Integration≻Average Value≻Cylindrical
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Average Value of a Function in Cylindrical Coordinates
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Integrand
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Region:
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Inert Integral:
(Note automatic insertion of Jacobian.)
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Value
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Table 8.2.11(a) Solution by task template implementing the FunctionAverage command
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To implement a solution from first principles, evaluate the integral of over and divide by the volume computed in Example 8.1.22. To integrate over , use the visualization task template in Table 8.2.11(b).
Tools≻Tasks≻Browse:
Calculus - Multivariate≻Integration≻Visualizing Regions of Integration≻Cylindrical
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Evaluate and Graph
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, where
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Table 8.2.11(b) Integration of over by visualization task template
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Table 8.2.11(c) completes the solution from first principles.
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Copy and paste the value of
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Context Panel: Evaluate and Display Inline
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=
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Table 8.2.11(c) Completion of the solution from first principles
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