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  "body": "\n## Summary\n\nThe degree of exactness of a [[quadrature rule|ADSVMCY77A]] is the largest $d$ such that the rule is exact for all polynomials of degree $\\le d$.\nIt is the standard first measure of the quality of a rule: for smooth integrands, a high degree of exactness usually means a small error.\nA rule with $n$ nodes has degree of exactness at most $2n - 1$, and Gaussian quadrature reaches this bound.\n\n## Explanations\n\n### L1 human\n\nPolynomials are the simplest functions, so a good integration recipe should at least get them right.\nThe degree of exactness counts how far up the ladder $1, x, x^2, x^3, \\dots$ the recipe is exact.\nThe midpoint rule is exact for straight lines but not for $x^2$, so its degree is $1$.\nSimpson's rule, with three nodes, is exact even for cubics, so its degree is $3$.\n",
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