The same five points can produce very different integral estimates. Work through the trapezoidal rule and Simpson’s rule step by step, compare their absolute errors, and learn how error bounds guide your choice of subintervals. Then connect the methods to midpoint and Romberg integration and test your skills on a practice problem with a complete solution.
Error bounds tell students how accurate an approximation is. This Woody Calculus lesson compares alternating series error with Taylor remainder, explains the first omitted term rule, and shows how Taylor’s theorem controls polynomial approximation error.
