Trapezoid and Simpson Examples

Numerical Analysis · Axiom Academy

EXAMPLE Trapezoid and Simpson's Rule Compare numerical integration methods on the same integral Excellent work! You've completed this comparison example. Trapezoid Rule: Uses linear interpolation between endpoints. Simple but less accurate for curved functions. Simpson's Rule: Uses parabolic interpolation (3 points). More accurate for smooth functions—exact for cubics! Error comparison: Simpson's error was ~170× smaller than trapezoid error for this integral. Pattern: For functions with significant curvature, Simpson's Rule typically gives much better results with the same number of function evaluations. Simpson's Rule generally outperforms the Trapezoid Rule when functions are smooth and well-behaved!

This is the written version of the interactive lesson above. See the full Numerical Analysis course.