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:
\(\int^b_af(x)dx=h/3[(y_0+y_n)+4(y_1+y_3+y_5+..\)
\(+y_{n-1})+2(y_2+y_4+y_6+..+y_{n-2})]\)
This rule is known as Simpson’s One-third rule.
