Multiple integral

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The multiple integral is a generalization of the definite integral to functions of more than one real variable, for example, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in R2 are called double integrals, and integrals of a function of three variables over a region of R3 are called triple integrals.[1]

Contents

1 Introduction
2 Mathematical definition

2.1 Properties
2.2 Particular cases

3 Methods of integration

3.1 Integrating constant functions
3.2 Use of symmetry
3.3 Normal domains on R2

3.3.1 x-axis
3.3.2 y-axis
3.3.3 Example
3.3.4 Normal domains on R3

3.4 Change of variables

3.4.1 Polar coordinates
3.4.2 Cylindrical coordinates
3.4.
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