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For questions regarding computation and results related to integrals in at least 2 variables.

A multiple integral is a generalization of the usual integral in one dimension to functions of multiple variables in higher-dimensional spaces.

e.g., $$\int \int f(x,y) ~dx~dy$$ is an integral of a function over the two dimensional region.

The most common multiple integrals are double and triple integrals, involving two or three variables, respectively. Since the world has three spatial dimensions, many of the fundamental equations of physics involve multiple integration (e.g. with respect to each spatial variable).

Multiple integration of a function in $$~n~$$ variables: $$~f(x_1, x_2,\cdots, x_n)~$$ over a domain $$~D~$$ is most commonly represented by nested integral signs in the reverse order of execution (the leftmost integral sign is computed last), followed by the function and integrand arguments in proper order (the integral with respect to the rightmost argument is computed last). The domain of integration is either represented symbolically for every argument over each integral sign, or is abbreviated by a variable at the rightmost integral sign: $$\int \cdots \int_D f(x_1, x_2,\cdots, x_n)~~dx_1~\cdots~dx_n$$

Since the concept of an antiderivative is only defined for functions of a single real variable, the usual definition of the indefinite integral does not immediately extend to the multiple integral.

References:

https://en.wikipedia.org/wiki/Multiple_integral

https://brilliant.org/wiki/multiple-integral/