An Analytical Comparison of Definite Numerical Integration Methods: A Study on Efficiency and Accuracy

This study reviews definite numerical integration methods and provides an analytical comparison of different techniques used to compute integrals in the fields of applied mathematics and engineering. The primary goal of the research is to assess the efficiency and accuracy of each method in calculating definite integrals, with a focus on performance effectiveness when dealing with complex functions. A range of common methods, such as the trapezoidal rule, Romberg method, and Simpson's rule, were analyzed. The paper presents the results of numerical experiments conducted on a set of practical examples, with a detailed discussion of the challenges each method faces and its suitability for various applications. In conclusion, recommendations are provided for selecting the most appropriate method based on the required accuracy level and available computational resource.