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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Hope Enterprises provides training and work to people affected by homelessness, drugs, alcohol, poverty, mental health and other disadvantage, within Northamptonshire, UK. We are a Community Interest Company (or CiC) owned by Northampton Hope Centre, a charity which has been providing help to people in acute need with multiple disadvantage, since 1974. Any profits or surplus made by Hope Enterprises supports our charitable work.