2D Surface Integrals
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.