Integration by substitution can be derived from the fundamental theorem of calculus as follows. Let Æ and Ï be two functions satisfying the above hypothesis that Æ is continuous on I and Ïâ² is continuous on the closed interval [a,b] . Then the function Æ(Ï(t))Ïâ²(t) is also continuous on [a,b] . Hence the integrals.
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Aerial photo of Hope (2013) Hope is a city in southern Dickinson County, Kansas, United States. As of the 2010 census, the city population was 368. The motto of Hope is There Will Always Be Hope In Kansas, which is also the name of a song.