Line Integrals

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Line Integrals

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The operators BINTEGRAL and LINE_INTEGRAL are synonymous, and perform line integrations of scalar integrands.


The integral is always taken with respect to distance along the line or curve.


The basic form of the LINE_INTEGRAL operator is:


BINTEGRAL ( integrand, named_boundary )

LINE_INTEGRAL ( integrand, named_boundary )


The boundary specification may be omitted, in which case the entire outer boundary is implied.


2D Line Integrals


In 2D Cartesian geometry, LINE_INTEGRAL is the same as SURF_INTEGRAL.


In 2D cylindrical geometry, SURF_INTEGRAL will contain the 2*pi*r weighting, while LINE_INTEGRAL will not.


2D Line integrals may be further qualified by specifying the region in which the evaluation is to be made:


LINE_INTEGRAL ( integrand, named_boundary, named_region )


named_region must be one of the regions bounded by the selected boundary.


3D Line Integrals


3D Line integrals may be computed only on extrusion surfaces of the 3D domain.


LINE_INTEGRAL ( integrand, named_boundary, surface_number )

LINE_INTEGRAL ( integrand, named_boundary, named_surface )


The named_boundary must exist in the named_surface (ie, it must not have been excluded by LIMITED REGION commands).