# Guido Fubini Essay

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Fubini’s Theorem Guido Fubini, born 19 Jan 1879 in Venice, Italy, died 6 June 1943 in New York, USA, was a great mathematician that added a great theorem to the concept of calculus. Guido Fubini's father Lazzaro Fubini was a mathematics teacher at the Scuola Macchinisti in Venice. Guido Fubini came from a mathematical background and was influenced by his father towards mathematics when he was young. In 1896, Fubini entered the Scuola Normale Superiore di Pisa. There he was taught by Dini and Bianchi who quickly influenced Fubini to undertake research in geometry. He presented his doctoral thesis Clifford's parallelism in elliptic spaces in 1900. In October 1901 Fubini began teaching at the University of Catania in Sicily, and in 1908 Fubini moved to Turin where he taught both at the Politecnico and at the University of Turin. Fubini created a theorem very significant to our Calculus 3 class at Miramar college. His theorem makes it possible to change the order of integration with double integrals, which is used to find area under a plane. Fubini assumed that both integrals are less then infinite spaces. Therefore Fubini’s theorem states that if the absolute value of the function is finite, the order or integration doesn’t matter and can be reversed. If we integrate first in respect to x, then in respect to y, we get the same answer as if we integrated in terms of y first, then x. Putting dydx means that we need to re-arrange the limits of integration so the inside integral has limits for y, and the outside integral has the limits for x, and vice versa. In terms of the calculus 3 curriculum, this theorem makes it possible to evaluate double integrals in a much simpler way. This also makes it possible to change the limits of integration. This means looking at it horizontally versus horizontally, or vice versa. By graphing and visualizing we can