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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Freedomâs Home. A visit to the communities of Cumberland County will make you proud to be an American. Thereâs a patriotic spirit running through Fayetteville, Spring Lake, Hope Mills and the other Cumberland County municipalities that unites everyone who lives here, as well as those just passing through.