1-12 - Today 5.4 Indefinite Integrals 5.4 Net Change...

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January 12, 2005 Today § 5.4: Indefinite Integrals § 5.4: Net Change Theorem and applica- tions 1

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Definition. Let f be a continuous func- tion on an interval. The indefinite inte- gral of f is the most general antideriva- tive of f and it is denoted by f ( x ) dx. In particular the notation F ( x ) = f ( x ) dx means F ( x ) = f ( x ) .
Notation: Let f be a continuous func- tion on the interval [ a, b ]. b a f ( x ) dx is a number x a f ( t ) dt is an antiderivative of f whose value at a is 0 f ( x ) dx is the most general antiderivative of f

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Let f be a continuous function on [ a, b ]. Let F be an antiderivative of f . b a f ( x ) dx = F ( b ) - F ( a ) x a f ( t ) dt = F ( x ) - F ( a ) f ( x ) dx = F ( x ) + C
Table of indefinite integrals x n dx = x n +1 n + 1 + C ( n = - 1) 1 x dx = ln | x | + C e x dx = e x + C sin x dx = - cos x + C cos x dx = sin x + C sec 2 x dx = tan x + C sin x cos 2 x dx = sec x + C 1 1 + x 2 dx = arctan x + C 1 1 - x 2 dx = arcsin x + C

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A honeybee population starts with 100

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