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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Needham, Indiana. Needham is an unincorporated community in Needham Township, Johnson County, Indiana. History. Needham was platted in 1866 by Noah Needham. The post office was established as Needhams Station. The Needhams Station post office opened in 1866, and was officially renamed Needham in 1882.