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The synonymous prototype forms of surface integral functions in 2D are:

 

SINTEGRAL ( integrand, named_boundary )

SURF_INTEGRAL ( integrand, named_boundary )

 

Here named_boundary may be specified by name, or it can be omitted, in which case the entire outer boundary of the domain is implied.

In two-dimensional Cartesian problems, the surface element is formed by extending the two-dimensional line element a single unit in the Z-direction, so that the surface element is dl*1.  In this case, the surface integral is the same as the line integral.

 

In two-dimensional cylindrical problems, the surface element is formed as 2*pi*r*dl, so the surface integral is NOT the same as the line integral.

 

The region in which the evaluation is made can be controlled by providing a third argument, as in

 

SURF_INTEGRAL (  integrand, named_boundary, named_region )

 

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