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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Sponsored Topics. Hopewell is a Borough in Mercer County, New Jersey, United States. As of the United States 2010 Census, the borough population was 1,922. Hopewell was incorporated as a borough by an Act of the New Jersey Legislature on April 14, 1891, from portions of Hopewell Township, based on the results of a referendum held on March 21, 1891.