The Degree of Precision of A Quadrature Formula Def.5.2.The degree ofprecision of a quadrature formula is the positive integer n such that E[P ]0 for all polynomials P(x)of degree isn,but for which E[P]t0 for some polynomial P(x)of degree n+1. The form of E[P]can be anticipated by studying what happens when f(x)is a polynomial.Consider the arbitrary polynomial P(x)=ax+a+...+ax+ao of degree i. If isn,then P((x)=0 for allx,and P(x)=(n+1)a for all x. Thus the general form for the truncation error is E[f]=kf(D(c),where K is a suitably chosen constant and n is the degree of precision. Note:The definition of the degree of precision of a quadrature formula doesn't specify the integral interval The Degree of Precision of A Quadrature Formula ◼ Def. 5.2. The degree of precision of a quadrature formula is the positive integer n such that E[Pi ]=0 for all polynomials Pi (x) of degree i≤n, but for which E[Pn+1] ≠0 for some polynomial Pn+1(x) of degree n+1. The form of E[Pi ] can be anticipated by studying what happens when f (x) is a polynomial. Consider the arbitrary polynomial Pi (x)=aix i+ai-1x i-1+…+a1x+a0 of degree i. If i≤n, then Pi (n+1)(x)≡0 for all x, and for all x. ( 1) 1 1 ( ) ( 1)! n P x n a n n + + + = + Thus the general form for the truncation error is E[ f ]=K f (n+1)(c), where K is a suitably chosen constant and n is the degree of precision. Note: The definition of the degree of precision of a quadrature formula doesn’t specify the integral interval