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  "body": "\n## Summary\n\nNumerical integration is the computation of approximate values of [[definite integrals|04TMP0XGMJ]] from finitely many values of the integrand.\nIt is needed when an antiderivative has no closed form or when the integrand is only known at sample points.\nIt is also needed for integrals over domains of many dimensions.\nThe main tools are [[quadrature rules|ADSVMCY77A]], weighted sums of function values, together with error estimates based on the smoothness of the integrand.\n\n## Explanations\n\n### L1 human\n\nThe integral of a function is the area under its graph, but often there is no formula for it.\nNumerical integration estimates that area by measuring the height of the graph at some points and adding up suitable weighted heights.\nThe simplest example cuts the interval into strips and replaces each strip by a trapezoid.\nFor $\\int_0^1 e^{-x^2}\\, dx$, which has no elementary antiderivative, such methods give $0.7468\\ldots$ to any accuracy one wants.\n",
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