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→Multiple integrals: Add picture of double integral
==Multiple integrals==
==Multiple integrals==
[[Image:DoubleIntegral.png|right|thumb|200px|A double integral gives the volume under a function over a given area - here, the area under the function (at top) within a square.]]
Multiple integrals are integrals extended to higher dimensions. Just like a definite integral gives the area under a 2-dimensional function, a double integral gives the volume under a three-dimensional function, and a triple integral gives the four-dimensional volume under a four-dimensional function. An ordinary integral is integrated over a single variable, such as x; similarly, a double integral is integrated over a two-dimensional area, usually written A; and a triple integral is integrated over a three-dimensional volume, usually written V.
Multiple integrals are integrals extended to higher dimensions. Just like a definite integral gives the area under a 2-dimensional function, a double integral gives the volume under a three-dimensional function, and a triple integral gives the four-dimensional volume under a four-dimensional function. An ordinary integral is integrated over a single variable, such as x; similarly, a double integral is integrated over a two-dimensional area, usually written A; and a triple integral is integrated over a three-dimensional volume, usually written V.
:A double integral: <math>\iint\limits_D f(x,y) dA</math>
:A double integral: <math>\iint\limits_D f(x,y) dA</math>