A Proposed Method for Numerical Integration

The main objective of this paper is to propose a numerical integration method that provides improved estimates as compared to the Newton-Cotes methods of integration. The method is an extension of trapezoidal rule where after segmentation, the top part of each segment was further subdivided into rectangles and/or squares and triangles (approximate). The area of each segment is then obtained as the sum of areas of these geometric shapes and the area of the down part of the segments which is usually a rectangle. The process resulted in an improved formula for numerical integration which we derived in the paper. The proposed method was compared with some Newton-Cotes methods of integration and it outperformed. With the proposed method, one can provide estimates with predetermined desired absolute relative true errors.