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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Solve for
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Write the equation and press the Enter key.
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Context Panel: Solve≻Obtain Solutions for≻
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Context Panel: Assign to a Name≻
(Thus, and .)
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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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Iterate in the order via the template in the Calculus palette
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Calculus palette: Iterated double-integral template
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Context Panel: Evaluate and Display Inline
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Iterate in the order via the template in the Calculus palette
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Calculus palette: Iterated double-integral template
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Context Panel: Evaluate and Display Inline
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The task template in Table 6.2.1(a) iterates in the order . The upward-pointing arrow in the left-hand graph indicates that the inner (first) integration is in the -direction. The right-hand image contains a graph of the volume computed by the integral. Since the height of the region in the graph is the constant 1, the volume and the area are the same number.
Tools≻Tasks≻Browse:
Calculus - Multivariate≻Integration≻Visualizing Regions of Integration≻Cartesian 2-D
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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 6.2.1(a) Iteration in the order via visualization task-template
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The task template in Table 6.2.1(b) iterates in the order . The right-pointing arrow in the left-hand graph indicates that the inner (first) integration is in the -direction. The right-hand image contains a graph of the volume computed by the integral. Since the height of the region in the graph is the constant 1, the volume and the area are the same number.
Tools≻Tasks≻Browse:
Calculus - Multivariate≻Integration≻Visualizing Regions of Integration≻Cartesian 2-D
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Evaluate and Graph
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Area Element
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,
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Value of Integral
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Table 6.2.1(b) Iteration in the order via visualization task-template
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