Multiple integral

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Calculus
${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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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 ${\displaystyle \mathbb {R} ^{2}}$ (the real-number plane) are called double integrals, and integrals of a function of three variables over a region in ${\displaystyle \mathbb {R} ^{3}}$ (real-number 3D space) are called triple integrals.^[1] For repeated antidifferentiation of a single-variable function, see the Cauchy formula for repeated integration.