Question

14: For a definite integral of any third order
polynomial, the two-point Gauss quadrature rule will
give the same results as the​

Answer 1

Given  : For a definite integral of any third order  polynomial, the two-point Gauss quadrature rule will  give the same results as the​

To Find : Correct option  

(A) 1-segment trapezoidal rule

(B) 2-segment trapezoidal rule

(C) 3-segment trapezoidal rule

(D) Simpson’s 1/3 rule

Solution:

For integrating any third order polynomial, the two-point Gauss quadrature rule will give the  same results as Simpson’s 1/3 rule.

Because of the 1/3 factor Simpson's rule is also referred to as Simpson's 1/3 rule

two-point Gauss quadrature rule also known as Gauss-Legendre quadrature rule.

Both these rules two-point Gauss quadrature rule  and  Simpson’s 1/3 rule

exactly integrate polynomials of third order  or less.

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the gaussian quadrature by using n+1 points is exact for polynomials of degree k satisfying is K= 2n+ 1

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