Series and Multiple Integrals

A multiple integral is a definite integral of a function of several real variables in mathematics (specifically multivariable calculus), such as f(x, y) (x, y, z). Double integrals are integrals of a function of two variables over a region in displaystyle mathbb R 2mathbb R 2 (the real-number plane), and triple integrals are integrals of a function of three variables over a region in displaystyle mathbb R 3mathbb R 3 (real-number 3D space). [1] See the Cauchy formula for repeated integration for multiple integrals of a single-variable function.

KEY FEATURE

The integral of a function of one variable over an interval yields an area, whereas the double integral of a function of two variables over a region yields a volume.

Triple integrals are used for functions with three variables, and so on. Such constructions are useful in calculating the net change in a function as a result of changes in its input values.

For each argument over each integral sign, the domain of integration is either represented symbolically or abbreviated by a variable at the rightmost integral sign.

The Cauchy formula for repeated integration can be used to calculate multiple integrals of a function in a single variable.

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