Computational Study of Numerical Integration in Physics Applications Using Trapezoidal and Simpson's Methods

This research conducts a comprehensive evaluation of the efficiency and accuracy of two widely-used numerical integration methods, the Trapezoidal Rule and Simpson's Rule, within the context of solving physics-related problems. The study focuses on four representative cases: the calculation of kinetic energy, the determination of electric field strength, the work done by an ideal gas, and the gravitational potential energy. The performance of these methods is analyzed through key metrics such as convergence behavior, error magnitude, and computational time. The findings reveal that Simpson's Rule consistently delivers higher accuracy compared to the Trapezoidal Rule, especially for functions exhibiting non-linear characteristics. This highlights Simpson's Rule as a preferred method for complex physical problems, while the Trapezoidal Rule remains effective for simpler cases requiring lower computational overhead.