= Interpolatory quadrature
{title2=$Q(f)=\int_a^bp_n(x)\,dx$}
= Interpolatory quadrature rule
{synonym}
An <interpolatory quadrature> approximates a <definite integral> by exactly integrating the <interpolation polynomial> through prescribed sampled values. For distinct <quadrature nodes> $x_0,\ldots,x_n$, its <quadrature weights> are $W_j=\int_a^b\ell_j(x)\,dx$, where $\ell_j$ are the <Lagrange cardinal polynomials>. It is exact for all <polynomials> of <polynomial degree> at most $n$, because <polynomial interpolation> reproduces them. <Newton-Cotes quadrature> adds equal spacing of the <quadrature nodes>.
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