The divergence of F:
Implement the integral of over the interior of :
=
To compute the flux through , note that there are four boundaries, the coordinate planes and the plane . Table 9.8.10(a) lists the faces, the unit normal on that face, the expression for , and the value of on that face.
Face
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value of
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Table 9.8.10(a) on the four faces of
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The only face through which there is nonzero flux is the plane . This flux is given by
=
The total flux through the boundaries of matches the volume integral of the divergence.