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How does Simpson's rule work?

Simpson's rule is a Newton-Cotes formula for approximating the integral of a function using quadratic polynomials (i.e., parabolic arcs instead of the straight line segments used in the trapezoidal rule). Simpson's rule can be derived by integrating a third-order Lagrange interpolating polynomial fit to the function at three equally spaced points.

What is The Simpsons formula?

The Simpson’s rule formula states that the curve will be divided into n equal vertical parts. Then each part is taken and its area is calculated. We divide the area into n equal segments of width Δx. The approximate area is given by the following.


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