Question 5
(25 Marks)
(a) How do you use the Legendre polynomial Ln+i of degree n+1 to construct & quadrature rule on a finite interval (a, b) with degree of precision 2n + 1 and n + 1 points?
(b) Prove that the degree of precision of a Newton Cotes quadrature rule using n + 1 points is not smaller than n.
c) Prove that the degree of precision of a quadrature rule using n+ 1 points is not more than 2n + 1.