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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Parke County lies in the western part of the U.S. state of Indiana along the Wabash River. The county was formed in 1821 out of a portion of Vigo County. According to the 2010 census, the population was 17,339, an increase of 0.6% from 17,241 in 2000. The county seat is Rockville.