Numerical Methods Simpsons 13 rule is based on A Substitutin

Numerical Methods

Simpson\'s 1/3 rule is based on A) Substituting a 2nd-order interpolating polynomial for the data or the function. B) Substituting a 3rd-order interpolating polynomial for the data or the function. C) Multiple applications of the trapezoidal rule with smaller and smaller steps. D) Substituting a 1st-order interpolating polynomial for the data or the function.

Solution

Since, Simpson’s 1/3 rule is an extension of Trapezoidal rule where the integrand is approximated by a second order polynomial.

hence, option A is correct. i.e. substituting a 2nd-order interpolating polynomial for the data or the function