Degree of exactness of a quadrature rule

Summary

The degree of exactness of a quadrature rule is the largest $d$ such that the rule is exact for all polynomials of degree $\le d$. It is the standard first measure of the quality of a rule: for smooth integrands, a high degree of exactness usually means a small error. A rule with $n$ nodes has degree of exactness at most $2n - 1$, and Gaussian quadrature reaches this bound.