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Card 11 / 12:
Fubini’s theorem
if f ( x , y ) is a function of two variables that is continuous over a rectangular region R = { ( x , y ) ∈ ℝ 2 | a ≤ x ≤ b , c ≤ y ≤ d } , then the double integral of f over the region equals an iterated integral, ∬ R f ( x , y ) d y d x = ∫ a b ∫ c d f ( x , y ) d x d y = ∫ c d ∫ a b f ( x , y ) d x d y
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