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 declared line or curve path (positive in the path direction).


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).