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2311lectureoutline5.3

# 2311lectureoutline5.3 - F be any antiderivative of f that...

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MAC2311, Calculus I 5.3 The Fundamental Theorem of Calculus The Fundamental Theorem of Calculus establishes a connection between the two branches of calculus: differential calculus and integral calculus. This theorem provides us with a much simpler method for evaluating definite integrals then using the limit definition for a definite integral. The Fundamental Theorem of Calculus: Let f be continuous on [a, b], and let
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Unformatted text preview: F be any antiderivative of f , that is F’ = f . Then… ( ) ( ) ( ) b a f x dx F b F a =-& . Graphically, the Fundamental Theorem of Calculus means that the rate of change of the area function is the height of the original function. The Fundamental Theorem guarantees that every continuous function f on I has an antiderivative on I . (Not that it’s always easy to find…) Try exercises 20, 22, 26, 30, 32, 38 and 65 on pages 388-389 in your text....
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