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has gloss | eng: In calculus an iterated integral is the result of applying integrals to a function of more than one variable (for example f(x,y) or f(x,y,z)) in a way that each of the integrals considers some of the variables as given constants. For example, the function f(x,y), if y is considered a given parameter can be integrated with respect to x, \int f(x,y)dx. The result is a function of y and therefore its integral can be considered. If this is done, the result is the iterated integral :\int\left(\int f(x,y)\,dx\right)\,dy. It is key for the notion of iterated integral that this is different, in principle, to the multiple integral :\int\int f(x,y)\,dx\,dy. Although in general these two can be different there is a theorem that, under very mild conditions, gives the equality of the two. This is Fubini's theorem. |
lexicalization | eng: iterated integral |
instance of | e/Lists of integrals |
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