Introduction to Quadrature The goal is to approximation the definite integral offx)over the interval [a,b]by evaluatingfx)at a finite number of sample points. Def.5.1.Suppose that a=xo<x<...<xb.A formula of the form Qf1-w/(x)-w/(x)+wf(x)++wf(x) with the property that f()d+ is called a numerical integration or quadrature formula.The term E[f] is called the truncation error for integration.The values are called the quadrature nodes,and ware called the Weights.Introduction to Quadrature ◼ The goal is to approximation the definite integral of f(x) over the interval [a, b] by evaluating f(x) at a finite number of sample points. ◼ Def. 5.1. Suppose that a=x0<x1<…<xM =b. A formula of the form with the property that is called a numerical integration or quadrature formula. The term E[ f ] is called the truncation error for integration. The values are called the quadrature nodes, and are called the Weights . 0 0 1 1 0 [ ] ( ) ( ) ( ) ( ) M k k M M k Q f w f x w f x w f x w f x = = = + + +  ( ) [ ] [ ] b a f x dx Q f E f = +  0 { }M k k x = 0 { }M wk k=