<< Click to Display Table of Contents >> 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 twodimensional Cartesian problems, the surface element is formed by extending the twodimensional line element a single unit in the Zdirection, so that the surface element is dl*1. In this case, the surface integral is the same as the line integral.
In twodimensional 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.