Numerical Integration - Interactive Visualization

Numerical integration approximates definite integrals using finite summation. The trapezoid rule uses first-order polynomial fits. Simpson's rule uses second-order, dramatically reducing error. Gaussian quadrature uses strategically placed points (Gauss-Legendre nodes) to achieve polynomial exactness far beyond its apparent simplicity - n points exactly integrate polynomials up to degree 2n-1.

• Choose from sin, x², exp(-x²), |x| and integration bounds
• Compare trapezoid, Simpson, and Gaussian quadrature on the same function
• Adjust n (number of panels/points) to see error decrease
• See error vs n convergence rate: O(h²) vs O(h⁴) vs exponential
• Foundation for Monte Carlo integration, expectation computation, and normalizing constants

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