Simpson's rule
![Simpson's rule can be derived by approximating the integrand f (x) (in blue) by the quadratic interpolant P(x) (in red).](/Images/godic/202502/11/Simpsons_method_illustration.svg1553.png")
![An animation showing how Simpson's rule approximation improves with more strips.](/Images/godic/202502/11/Simpsonsrule21553.gif")
In numerical analysis, Simpson's rule is a method for numerical integration, the numerical approximation of definite integrals. Specifically, it is the following approximation:
Simpson's rule also corresponds to the three-point Newton-Cotes quadrature rule.