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1 Lecture 17 : Fundamental Theorems of Calculus, Riemann Sum By looking at the definitions of differentiation and integration, one may feel that these notions are totally different. Even the geometric interpretations do not give any idea that these two notions are related. In this lecture we will discuss two results, called fundamental theorems of calculus, which say that differentiation and integration are, in a sense, inverse operations. Theorem 17.1: (First Fundamental Theorem of Calculus) Let f be integrable on [a, b]. Rx For a ≤ x ≤ b, let F (x) = a f (t)dt. Then F is continuous on [ ...
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