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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Anderson is a city in and the county seat of Madison County, Indiana, United States. It is the principal city of the Anderson, Indiana Metropolitan Statistical Area which encompasses Madison County. Anderson is the headquarters of the Church of God and home of Anderson University, which is affiliated with that denomination. Highlights of the city include the historic Paramount Theatre and the Gruenewald Historic House. The population was 56,129 at the 2010 census. This is down from 70,000 in 197