MATLAB Code Implementation for Numerical Integration

This document presents several source code implementations for numerical integration methods in MATLAB. The available algorithms include: Composite Trapezoidal Rule for integration, Simpson's family of formulas for numerical integration, Newton-Cotes series formulas for integration, Gaussian quadrature formulas, Gauss-Radau integration formulas, and Gauss-Lobatto integration formulas. These implementations provide ready-to-use MATLAB code for various numerical integration scenarios. Implementation Details: Each function follows MATLAB best practices with proper input validation and error handling. The algorithms demonstrate different approaches to numerical integration - from simple trapezoidal approximations to more sophisticated Gaussian quadrature methods that provide higher accuracy with fewer function evaluations. The code includes adaptive step sizing where appropriate and handles both definite integrals and improper integrals through transformation techniques. Key Features: All implementations support vectorized operations for efficient computation, include detailed documentation within the code, and provide examples of usage for common integration problems. The functions are optimized for performance while maintaining numerical stability across different integration intervals and function types.