Quadrature Formulas Based on Polynomial Interpolation There exists a unique polynomial Pux)of degree <M passing through the M+1 equally spaced points {(xf()).When this polynomial is used to approximate f(x)over [a,b],and then the integral off(x)is approximated by the integral of Px),the resulting formula is called a Newton-Cotes quadrature formula When the sample points xo-a and xb are used,it is called a closed Newton-Cotes formula. Quadrature Formulas Based on Polynomial Interpolation ◼ There exists a unique polynomial PM(x) of degree ≤M passing through the M+1 equally spaced points . When this polynomial is used to approximate f (x) over [a,b], and then the integral of f (x) is approximated by the integral of PM(x), the resulting formula is called a Newton-Cotes quadrature formula. When the sample points x0 =a and xM =b are used, it is called a closed Newton-Cotes formula. 0 {( , ( ))}M k k k x f x =