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  "body": "\n## Summary\n\nA multiple integral is the integral of a real function of $n$ real variables over a region of $\\R^n$.\nIt extends the one-variable [[Riemann integral|0W29TBTY12]] from intervals to boxes and to more general bounded sets.\nThe [[double integral|0WAR4F23B4]] and the [[triple integral|0698M7C7AX]] are the cases $n = 2$ and $n = 3$.\nMultiple integrals give areas, volumes, masses, centres of mass and probabilities of random vectors.\n\n## Explanations\n\n### L1 human\n\nCut a region of space into many small boxes.\nIn each box, multiply a value of the function by the volume of the box, and add up all these products.\nWhen the boxes get smaller and the sums settle to one number, that number is the multiple integral.\nFor example, the integral of the constant $1$ over the unit cube $[0, 1]^3$ is its volume, $1$.\nIn practice one often computes a multiple integral as an [[iterated integral|0WZCHE1ZF9]], one variable at a time.\n",
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