The VOL_INTEGRAL (alias INTEGRAL) operator in Cylindrical geometry is weighted by 2*PI*R, representing the fact that the equations are solved in a revolution around the axis.

An integral over the cross-sectional area of a region may be requested by the operator AREA_INTEGRAL.  This form differs from VOL_INTEGRAL in that the 2*PI*R weighting is absent.

Similarly, the operator SURF_INTEGRAL will form the integral over a boundary, analogous to the LINE_INTEGRAL operator, but with an area weight of 2*PI*R.