الخلاصة

In this paper ,we used search method for calculating the approximate values of double integrals , when its integrands continuous and we choose rules (Trapezoidal and mid-point)because the approximate values resulting from the use of Trapezoidal rule be faster closer to the real value of the integrals compared to another formulas of Newton-Cotes formulas ,but for the rule mid-point we can use it in the calculation of continuous integrand or non-continuous integrands in the region of integration because it is not use the values of function of integration in both ends of the integration period and the symbol of this rule is .We choose ( the number of subintervals of )is equal to (number of subintervals of )and we improved the results by applying Aitken accelerate with and denote to the method by , where the symbol A indicates to the Aitken’s acceleration method and (indicates to the mid-point rule on the external dimension and Trapezoidal rule on the internal dimension ).