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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2018 Lilly Endowment Community Scholarship Program Opens. Posted on August 1, 2017August 1, 2017 by Rockport, Indiana â The Spencer County Community Foundation is now accepting applications online for the 2018 Lilly Endowment Community Scholarship Program. The scholarship is open to Indiana high school students who will be graduating from an accredited Indiana high school by June 2018.