Equal Tangent Length Partitioning for High-Precision Numerical Integration

In this study we develop a novel approach for improvement of the precision of numerical integration by using equal tangent slopes in order to partition the integration interval. As a result, two new composite numerical integration formulas are derived. Using continuous function properties, it is possible to analyze the error and convergence of these formulas. A practical example confirms the effectiveness of this method in improving the accuracy of numerical integration. Additionally, the paper delves into the convergence properties and the error reduction capabilities of the new formulas compared to the traditional trapezoidal and Simpson’s rules. The limitations of the developed approach are briefly discussed.