Numerical Approximation of Definite Integrals and Convergence Behaviour

Mathematics — 2025, Undergraduate

This study examined the numerical approximation of definite integrals and the convergence behaviour of common quadrature rules. Representative integrals were approximated by rectangular, trapezoidal, and Simpson-like rules at increasing partitions, and errors were analysed. The findings revealed that all methods converged to the true integral as partitions increased, with higher-order methods converging faster, while error magnitudes depended on function smoothness. The study observed predictable error patterns. It recommends selecting quadrature rules based on required accuracy and function properties.

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