Derivation of General Moment Form of Green’s Theorem Curve Integral from Vector Product

In this paper, the general moment form of Green’s Theorem curve integral, for the calculation of the area and moments values of the planar region enclosed by arbitrary curve, is derived from the numerical version of its belonging moment integrals that are obtained from discrete vector product and differential vector product properties. Then, all six area and moments integrals are derived in a new, uniform integral form, for calculation of: area itself, its static moments, area centroids and moments of inertia of observed enclosed area region below arbitrary curve, based on the initial Green’s theorem curve integral for the calculation of the area enclosed by general curve, and the properties of discrete and differential vector products.