Table 8.1.26(a) provides a solution by a task template that integrates in cylindrical coordinates and draws the region of integration.
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 8.1.26(a) Task template integrating in spherical coordinates
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Since the iteration order can be taken as , the task template in Table 8.1.26(a), using the MultiInt command from the Student MultivariateCalculus package, applies.
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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>
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Value:
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Stepwise Evaluation:
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Table 8.1.26(b) Task template implementing the MultiInt command iterating in the order
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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 8.1.26(c) provides a solution from first principles.
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Calculus Palette:
Iterated triple-integral template
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Context Panel: Evaluate and Display Inline
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Table 8.1.26(c) Integration via first principles
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