The divergence of F, which is , is integrated over subregions , as per Figure 9.10.9(a), in Table 9.10.9(a).
Define as
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Context Panel: Assign to a Name≻
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Integrate over the region
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Calculus palette: Iterated definite-integral template
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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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Table 9.10.9(a) Integral of over the region
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The flux of F through the two bounding curves and is obtained in Table 9.10.9(b). The passage around this closed contour is in the counterclockwise direction.
Initialize
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Tools≻Load Package: Student Vector Calculus
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Loading Student:-VectorCalculus
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Tools≻Tasks≻Browse: Calculus - Vector≻
Vector Algebra and Settings≻
Display Format for Vectors
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Press the Access Settings button and select
"Display as Column Vector"
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Display Format for Vectors
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Define the vector field F
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Write the vector field as a free vector.
Context Panel: Evaluate and Display Inline
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Context Panel: Student Vector Calculus≻Conversions≻To Vector Field
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Context Panel: Assign to a Name≻F
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Obtain the flux of F through and
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Apply the Flux command and press the Enter key.
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Context Panel: Evaluate Integral
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Table 9.10.9(b) Flux of F through and
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The flux of F through the bounding curves , is obtained in Table 9.10.9(c). The passage around this inner loop is clockwise, consistent with the orientation of the outer loop.
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Apply the Flux command and press the Enter key.
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Context Panel: Evaluate Integral
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Table 9.10.9(c) Flux of F through the bounding curves
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The total flux through the boundaries of the region is then = .