Initialize
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Tools≻Load Package:
Student Multivariate Calculus
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Loading Student:-MultivariateCalculus
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Context Panel: Assign Name
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Context Panel: Assign Name
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Context Panel: Assign Name
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Context Panel: Assign Name
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Access the MultiInt command via the Context Panel
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Write , the name of the integrand.
Context Panel: Evaluate and Display Inline
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Context Panel: Student Multivariate Calculus≻Integrate≻Iterated
Fill in both panes (see Figures 5.3.(1, 2)) and select "integral" for the Output
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Context Panel: Approximate≻10 (digits)
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Table 5.3.9(b) illustrates the visualization task template keyed to iterate in the order .
Tools≻Tasks≻Browse:
Calculus - Multivariate≻Integration≻Visualizing Regions of Integration≻
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Evaluate and Graph
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Area Element
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Value of Integral
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Table 5.3.9(b) Visualizing and the resulting volume for iteration in the order
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The horizontal arrow in the left-hand graph indicates that the iteration is in the order , whereby the first (or inner) integration is in the horizontal direction, from the leftmost boundary curve to the rightmost. Because the integrand is positive, the double integral calculates the volume below the surface but above the plane . The solid whose volume is thereby calculated is seen in the right-hand graph.
The detailed analytic results below are obtained via the palettes and Context Panel.
Iterate in the order
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Calculus palette: Template for definite iterated double integral
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Context Panel: Evaluate and Display Inline
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Context Panel: Approximate≻10 (digits)
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Display the iterated integrals
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Calculus palette: Template for definite iterated double integral
Context Panel: 2-D Math≻Convert To≻Inert Form
Press the Enter key
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Context Panel: Evaluate Integral
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Note: The calculations by which the expression for is obtained are as follows.
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Context Panel: Solve≻Obtain Solutions for≻
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Context Panel: Rationalize
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