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In mathematics , a multiple integral is a definite integral of a function of several real variables, for instance, f or f. Integrals of a function of two variables over a region in R 2 {\displaystyle \mathbb {R} ^{2}} are called double integrals, and integrals of a function of three variables over a region in R 3 {\displaystyle \mathbb {R} ^{3}} are called triple integrals. For multiple integrals of a single-variable function, see the Cauchy formula for repeated integration.
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