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Unformatted text preview: Section 4.10: Antiderivatives The antiderivative of ′ f x ( 29 is f x ( 29 . In other words, if ′ f x ( 29 is known, antidifferentiate to determine f x ( 29 . The most general antiderivative of ′ f x ( 29 should include + c , where c is an arbitrary constant. If the arbitrary constant can be determined, then f x ( 29 is a particular antiderivative. Table of Antidifferentiation Formulas Derivative, ′ f x ( 29 Antiderivative, f x ( 29 , (most general) x n , n ≠  1 x n + 1 n + 1 + c cos x sin x + c sin x cos x + c sec 2 x sec x tan x sec x + c csc 2 x cot x + c csc x cot x csc x + c Example. Find the most general antiderivative of ′ f x ( 29 = x 20 + x 7 3 14 . Solution. f x ( 29 = x 20 + 1 20 + 1 + x 7 + 1 3 7 + 1 ( 29 14 x + c f x ( 29 = x 21 21 + x 8 24 14 x + c Check: ′ f x ( 29 = d dx f x ( 29 = d dx x 21 21 + x 8 24 14 x + c = 21 x 20 21 + 8 x 7 24 14 + = x 20 + x 7 3 14 Example. Find the most general antiderivative of ′ f θ ( 29 = 6...
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This note was uploaded on 01/12/2010 for the course MATH 44245 taught by Professor Famiglietti during the Fall '07 term at UC Irvine.
 Fall '07
 FAMIGLIETTI
 Math, Antiderivatives, Derivative

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