Question

Simpson's one third rule with proof​

Answer 1

Answer:

Simpson’s 1/3rd rule is an extension of the trapezoidal rule in which the integrand is approximated by a second-order polynomial. Simpson rule can be derived from the various way using Newton’s divided difference polynomial, Lagrange polynomial and the method of coefficients. Simpson’s 1/3 rule is defined by:

∫ab f(x) dx = h/3 [(y0 + yn) + 4(y1 + y3 + y5 + …. + yn-1) + 2(y2 + y4 + y6 + ….. + yn-2)]

This rule is known as Simpson’s One-third rule.

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Answer 2

The approximate equality in the rule becomes exact if f is a polynomial up to quadratic degree. If the 1/3 rule is applied to n equal subdivisions of the integration range [a,b], one obtains the composite Simpson's rule. Points inside the integration range are given alternating weights 4/3 and 2/3.