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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Lake County, Indiana. Lake County is a county located in the U.S. state of Indiana. In 2010, its population was 496,005, making it Indiana's second-most populous county. The county seat is Crown Point. This county is part of Northwest Indiana and the Chicago metropolitan area, and contains a mix of urban, suburban and rural areas.