Abstract: The area coordinate method has been successfully applied to construct triangular elements. Recently, the area coordinate method was also applied to construct quadrilateral elements and the area coordinate theory for quadrilateral elements was systematically developed in Ref.1. This paper is the sequel to Ref.1. In this paper, the differential and integral formulas for area coordinates in quadrilateral elements are presented. Consequently, the numerical integration method which must be used in the formulation of stiffness matrix in isoparametric elements can now be discarded.