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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Crane is a town in Perry Township, Martin County, Indiana, United States. The population was 184 at the 2010 census.It was named in 1943 for William M. Crane and is adjacent to the Naval Surface Warfare Center Crane Division.rane is a town in Perry Township, Martin County, Indiana, United States. The population was 184 at the 2010 census.