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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Mount Hope (GNIS FID: 1065071) is a populated place located in Holmes County at latitude 40.624 and longitude -81.785. The elevation is 1,260 feet. Mount Hope appears on the Berlin U.S. Geological Survey Map. Holmes County is in the Eastern Time Zone (UTC -5 hours). Holmes County: Cities & Towns | ZIP Codes | Schools | Features (airports, churches, hospitals, etc.