"数值积分算法与 MATLAB 实现在定积分计算中的应用"

The graduation thesis entitled "Numerical Integration Algorithms and MATLAB Implementation" focuses on the problem of approximating definite integrals when the original function is too complex to be solved analytically. In such cases, numerical integration provides an effective approach to obtaining approximate values. The field of numerical integration is an important branch of numerical analysis, and exploring methods for approximating integrals has practical significance. This thesis starts by discussing the motivation behind numerical integration and provides a detailed introduction to several important methods. The Newton-Cotes quadrature formula is introduced in detail, along with high-precision numerical integration formulas such as Romberg's method and Gauss-Legendre quadrature. Theoretical analysis of these numerical integration algorithms is conducted, followed by the implementation of these algorithms using the MATLAB software. The thesis includes examples and comparisons of the various quadrature formulas, analyzing and comparing their computational errors. The overall goal is to evaluate the accuracy and efficiency of different numerical integration algorithms implemented in MATLAB. Keywords: numerical integration, Newton-Cotes quadrature formula, high-precision quadrature formula, MATLAB software. In conclusion, the graduation thesis "Numerical Integration Algorithms and MATLAB Implementation" provides a comprehensive exploration of various numerical integration methods. By implementing these algorithms using MATLAB, the thesis demonstrates their effectiveness in approximating definite integrals. The analysis and comparison of computational errors provide insights into the accuracy and efficiency of different numerical integration algorithms. Overall, this thesis contributes to the understanding and application of numerical integration algorithms for solving complex integration problems.