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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The eclectic community of New Hope is the gay-friendly centerpiece of Bucks County's breathtaking countryside. New Hope celebrates the LGBT community with the annual Pride Week and Parade, an annual celebration held each May throughout the downtown area.