Table 7.6.8(a) provides a solution by a visualization task template.
Tools≻Tasks≻Browse:
Calculus - Multivariate≻Integration≻Visualizing Regions of Integration≻Spherical
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Evaluate and Graph
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Volume Element
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, where
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Table 7.6.8(a) Solution by visualization task template
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In Table 7.6.8(a), transparency has been applied to the graph via its Context Panel.
Table 7.6.8(b) provides a solution by a task template that embodies the MultiInt command from the Student MultivariateCalculus package. It iterates in just the order , although the command itself will iterate in any of the six possible orders.
Tools≻Tasks≻Browse:
Calculus - Multivariate≻Integration≻Multiple Integration≻Spherical
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Iterated Triple Integral in Spherical Coordinates
( = colatitude, measured down from -axis)
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Integrand:
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Region:
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Inert Integral:
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Value:
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Stepwise Evaluation:
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Table 7.6.8(b) Solution by task template that embodies the MultiInt command
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Access the MultiInt command via the Context Panel
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Context Panel: Student Multivariate Calculus≻Integrate≻Iterated
Fill in the fields of the two dialogs shown below.
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Context Panel: Evaluate Integral
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Table 7.6.8(c) contains a solution from first principles, with the iterated integral being set via the iterated triple-integral template in the Calculus palette.
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Calculus palette: Iterated triple-integral template
(In the integrand, be sure to include the Jacobian for spherical coordinates.)
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Context Panel: Evaluate and Display Inline
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Table 7.6.8(c) Solution from first principles
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