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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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This note was uploaded on 03/09/2008 for the course CALC 1,2,3 taught by Professor Varies during the Spring '08 term at Lehigh University .
- Spring '08