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Simpson's 1/3 rule, also simply called Simpson's rule, is a method for numerical integration proposed by Thomas Simpson. It is based upon a quadratic interpolation and is the composite Simpson's 1/3 rule evaluated for n = 2 {\displaystyle n=2} .
Simpson's rule approximates an integral by performing quadratic interpolation between the endpoints and midpoint of the interval of integration. The formula for this method is. ∫ a b f (x) d x = h 6 (f (a) + 4 f (c) + f (b)), where h = b − a and c = (a + b) / 2. Here is a function to perform Simpson's rule just like we did for the trapezoid rule.
Simpson’s Rule, named after Thomas Simpson though also used by Kepler a century before, was a way to approximate integrals without having to deal with lots of narrow rectangles (which also implies lots of decimal calculations).
Simpson is best remembered for his work on interpolation and numerical methods of integration. However the numerical method known today as "Simpson's rule", although it did appear in his work, was something he learned from Newton as Simpson himself acknowledged.
Simpson's Rule is another numerical approach to finding definite integrals where no other method is possible.
Thomas Simpson FRS (20 August 1710 – 14 May 1761) was a British mathematician and inventor known for the eponymous Simpson's rule to approximate definite integrals.
Simpson's Rule is a numerical method for approximating the definite integral of a function. It involves dividing the interval of integration into smaller subintervals and using quadratic approximations to calculate the area under the curve.
