Presented in this paper is a computational approach that uses higher order Gaussian quadrature to improve the accuracy of the evaluation of an integral. The transformation from ξη space (standard Gaussian) to st space (higher order Gaussian) were shown throughout this paper. Not even that, the efficacy of this higher order Gaussian quadrature were tested by implementing and comparing it with standard Gaussian quadrature over the same integral. Results shown that the evaluation of an integral by using higher order Gaussian quadrature provide accurate and converge results compared to an integral using standard Gaussian quadrature.