<< Click to Display Table of Contents >> 2D Volume Integrals 

The synonymous prototype forms of volume integral functions in 2D are:
INTEGRAL ( integrand, region )
VOL_INTEGRAL ( integrand, region )
Here region can be specified by number or name, or it can be omitted, in which case the entire domain is implied.
In twodimensional Cartesian problems, the volume element is formed by extending the twodimensional cell a single unit in the Zdirection, so that the volume integral is the same as the area integral in the coordinate plane.
In twodimensional cylindrical problems, the volume element is formed as 2*pi*r*dr*dz, so that the volume integral is NOT the same as the area integral in the coordinate plane. For the special case of 2D cylindrical geometry, the additional operator
AREA_INTEGRAL ( integrand, region )
computes the area integral of the integrand over the indicated region (or the entire domain) without the 2*pi*r weighting.