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The synonymous prototype forms of volume integral functions in 3D are:
INTEGRAL ( integrand, region, layer )
VOL_INTEGRAL ( integrand, region, layer )
Here layer can be specified by number or name, or it can be omitted, in which case the entire layer stack is implied.
region can also be specified by number or name, or it can be omitted, in which case the entire projection plane is implied.
If region is omitted, then layer must be specified by name or omitted. If both region and layer are omitted, the entire domain is implied.
For example,
INTEGRAL(integrand, region, layer) means the integral over the subregion contained in the selected region and layer.
INTEGRAL(integrand, named_layer) means the integral over all regions of the named layer.
INTEGRAL(integrand, region) means the integral over all layers of the selected region.
INTEGRAL(integrand) means the integral over the entire domain.