# 1-10 - Calculus Let f be a continuous function on a b 1 The...

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January 10, 2005 Announcements Assigned reading for this week: § 5.3, 5.4 and 5.5 Homework #1 (Week 1 Problems) will be collected tomorrow, Tuesday, January 11 (Covers § 4.10, 5.1 and 5.2; see web for assignment) Today: § 5.3 The Fundamental Theorem of Calculus What is the relationship between diﬀerentiation and integration? The fundamental Theorem of Calculus Some applications 1

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The Fundamental Theorem of
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Unformatted text preview: Calculus Let f be a continuous function on [ a, b ]. 1. The function deﬁned by g ( x ) = Z x a f ( t ) dt is continuous on [ a, b ] and diﬀeren-tiable on ( a, b ). Moreover g ( x ) = f ( x ) . 2. If F is any antiderivative of f , i.e F = f in ( a, b ) then Z b a f ( t ) dt = F ( b )-F ( a ) . Find a function f and a number a such that 6 + Z x a f ( t ) t 2 dt = 2 √ x....
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1-10 - Calculus Let f be a continuous function on a b 1 The...

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