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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In October 1991, the Hope House came into existence and was located in two older homes provided by Thomas EQ Williams. The number of residents continued to grow and in 1997 with a HUD Federal funded grant, an old factory/warehouse located at 35 Pierson Street in Greenfield was purchased.