Abstract: Numerical integration method is the basic method in numerical analysis.The study of numerical integration is significant not only in mathematical theory but also in engineering practice. In order to solve the double integral approximation problem, this paper studies the calculation of double integral in rectangular area, and presents several formulas, including trapezoid quadrature formula, Simpson quadrature formula, the complex of the trapezoid quadrature formulas and complex of the Simpson quadrature formula. The validities of these formulas are proved by several typical examples.

Key words: Double Integral, Numerical integration, Trapezoidal quadrature formula, Simpson quadrature formula