What is Fubini's Theorem and How Does it Apply to Double and Iterated Integrals?

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Bruno Tolentino
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This integral: [tex]\int \int f(x,y) dx \wedge dy[/tex] is equal to this integral [tex]\int \int f(x,y) dx dy[/tex] ?
 
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If the region of integration is "type I" or "type II" then Fubini's theorem says they are the same. If the region of integration is not either of those, it can be divided into sub-regions that are.
 

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