Suppose F: [a, b] → Ris continuous and differentiable on [a, b] \ {c} for some ce [a, b]. Suppose there exists an integr

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Suppose F A B Ris Continuous And Differentiable On A B C For Some Ce A B Suppose There Exists An Integr 1 (16.86 KiB) Viewed 24 times

Suppose F: [a, b] → Ris continuous and differentiable on [a, b] \ {c} for some ce [a, b]. Suppose there exists an integrable f on [a, b] such that f(x) = F'() for re [a, b] \ {c}. Show that Sof= F(b) – F(a). (Hint: First show the case for c = a. Again Lemma 5.2.8 is your friend. The case c = b will be simliar. Force(a,b), breaks the integral into two then applies the cases that you have proved for the end points)