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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Hatfield is an unincorporated census-designated place in Luce Township, Spencer County, Indiana. Its population was 813 at the 2010 census. Hatfield was originally called Fair Fight, and under the latter name was laid out in 1883 by James Hatfield. A post office called Hatfield has been in operation since 1886. Hatfield is located at 37Â°54â²09â³N 87Â°13â²27â³W / 37.90250Â°N 87.22417Â°W / 37.90250; -87.22417. ^ US Board on Geographic Names.