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Calculus II Notes 5.4

# Calculus II Notes 5.4 - Calculus II-Stewart Dr Berg Spring...

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Calculus II- Stewart Dr. Berg Spring 2010 Page 1 5.4 5.4 Indefinite Integrals and the Net Change Theorem Antiderivatives play such an important role in integration that integral notation is commonly used to represent them. Definition f ( x ) dx = F ( x ) means d dx F ( x ) = f ( x ) and is called the indefinite integral of f . Example A cos x dx = sin x + C because d dx sin x + C ( ) = cos x . Notation: In keeping with existing notation and the FTC, f ( x ) dx a b = f ( x ) dx a b . Table of Common Indefinite Integrals c f ( x ) dx = c f ( x ) dx f ( x ) + g ( x ) [ ] dx = f ( x ) dx + g ( x ) dx k dx = kx + C x n dx = x n + 1 n + 1 + C sin x dx = cos x + C cos x dx = sin x + C sec 2 x dx = tan x + C csc 2 x dx = cot x + C sec x tan x dx = sec x + C csc x cot x dx = csc x + C Note: It is understood that each antiderivative is valid only for an interval. Therefore, the general anitiderivative for f ( x ) = 1

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Calculus II Notes 5.4 - Calculus II-Stewart Dr Berg Spring...

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