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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 crosssectional 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.