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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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: Evaluate Integral
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Tables 5.3.8(a, b) illustrate the visualization task template wherein a double integral can be iterated in either order. In the drop-down for area-element , select an ordering for the iteration. Then fill in the remaining fields as shown.
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 5.3.8(a) Visualizing and the resulting volume for iteration in the order
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The vertical arrow in the left-hand graph indicates that the iteration is in the order , whereby the first (or inner) integration is in the vertical direction, from the lowermost boundary curve to the uppermost. 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.
Table 5.3.8(b) shows the iteration in the opposite 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 5.3.8(b) Visualizing and the resulting volume for iteration in the order
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When integrating in the order , the first (or inner) integral is taken in the horizontal direction, as indicated by the arrow in the left-hand graph.
The detailed analytic results below are obtained via the palettes and Context Panel.
Iterate and
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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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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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