Multiple integral

Integral as area between two curves.
Double integral as volume under a surface z = 10 − (x2y2/8). The rectangular region at the bottom of the body is the domain of integration, while the surface is the graph of the two-variable function to be integrated.

In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z).

Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables over a region in (real-number 3D space) are called triple integrals.[1] For repeated antidifferentiation of a single-variable function, see the Cauchy formula for repeated integration.

  1. ^ Stewart, James (2008). Calculus: Early Transcendentals (6th ed.). Brooks Cole Cengage Learning. ISBN 978-0-495-01166-8.

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