Iterated integral

Type of integral of functions of multiple variables

In multivariable calculus, an iterated integral is the result of applying integrals to a function of more than one variable (for example f ( x , y) {\displaystyle f(x,y)} or f ( x , y , z) {\displaystyle f(x,y,z)}) in such a way that each of the integrals considers some of the variables as given constants. For example, the function f ( x , y) {\displaystyle f(x,y)} , if y {\displaystyle y} is considered a given parameter, can be integrated with respect to x {\displaystyle x} , ∫ f ( x , y) d x {\textstyle \int f(x,y)\,dx} . The result is a function of y {\displaystyle y} and therefore its integral can be considered.

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