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Unformatted text preview: Jenese Ortiz/Math 3A 3-9&10-09/Week #10/Session 1 Math 3A Worksheet #11 Topics Covered: Antiderivatives (Sec. 5.8) Lets Look at the following examples: 1. ? ? = 3 ? 2 2. ? ? = cos ? 3. ? ? = ? ? 4. ? ? = 1 ? Definition : A function F(x) is called an antiderivative of a function f(x) on an interval if F(x) = f(x) for all ? . If f(x) is continuous on the closed interval [ a,b ] and differentiable on the open interval (a,b) , with f(x) =0 for all ? ( , ? ) , then f is a constant on [ a,b ]. If F(x) and G(x) are antiderivatives of the continuous function f(x) on an interval I , then there exists a constant C so that: ? = ? + for all ? o Proof: Indeed if F(x) = f(x) then [ F(x)+C] = f(x)+(C) and (C) =0, thus ? = ? + Examples: 1. ? ? = 3 ? 5 2. ? ? = ? 2 + 2 ? 1 3. ? ? = 3 ? 2 2 ?...
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