# Multiple integral

definite integral over a multi-dimensional region of a function of several variables

In calculus and mathematical analysis, an integral is a way to calculate the limiting value a function with one variable will tend towards. Graphically, this can then be shown as the area under the graph of the function. In multivariate calculus, It is also possible to calculate integrals for functions with more than one variable. These integrals are commonly referred to as multiple integrals.

Volume under a surface - this is what a multiple integral for a function with two variables typically looks like.

An integral for a function with two variables over a two-dimensional region, called double integral, can be shown as a surface in three dimensional space. Similarly, an integral for a function with three variables over a three-dimensional region, called triple integral, can be thought of as a hypervolume.

A double integral can also be used to define an integral over an arbitrary surface (surface integral), just like a triple integral can be used to define an integral over an arbitrary volume (volume integral).[1][2][3]

## References

1. "List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-09-18.
2. "Multiple Integral | Brilliant Math & Science Wiki". brilliant.org. Retrieved 2020-09-18.
3. "Multiple Integrals | Boundless Calculus". courses.lumenlearning.com. Retrieved 2020-09-18.