Quadrature node ($x_i$)

A quadrature node is a point at which the integrand is sampled by a quadrature rule. Under the affine map $x=(a+b)/2+(b-a)t/2$ from $[-1,1]$ to $[a,b]$, a reference quadrature node $t_i$ becomes $x_i=(a+b)/2+(b-a)t_i/2$; for ordinary numerical integration, the corresponding quadrature weight is multiplied by $(b-a)/2$.