Simpson's Rule

This lecture introduces Simpson's rule as a three-point formula to approximate integrals over the interval [-1, 1]. By using three points (-1, 0, 1) and Lagrange basis polynomials, the weights for the formula are derived. The lecture demonstrates the accuracy of Simpson's rule for quadratic polynomials and extends the analysis to cubic polynomials. It concludes by discussing the error estimation for continuously differentiable functions using Simpson's rule.