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  "body": "\n## Summary\n\nA quadrature rule approximates a [[definite integral|04TMP0XGMJ]] $\\int_a^b f$ by a weighted sum $\\sum_i w_i f(x_i)$ of values of $f$ at fixed nodes.\nIt is the basic object of [[numerical integration|7HYF6YG0RS]] in one dimension.\nRules are compared by the polynomials they integrate exactly and by their error for smooth functions.\nNewton–Cotes rules use equally spaced nodes, and Gaussian rules use optimally placed nodes.\n\n## Explanations\n\n### L1 human\n\nTo estimate an area under a curve, one can measure the curve's height at a few chosen spots and combine the heights with fixed multipliers.\nThe spots are the nodes, the multipliers are the weights, and the recipe is the quadrature rule.\nThe same recipe is then used for every function.\nFor example, the midpoint rule measures the height once, at the centre, and multiplies it by the length of the interval.\n",
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