Section4_10_review

Section4_10_review - Section 4.10: Antiderivatives The...

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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 ( 29 = 6...
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Section4_10_review - Section 4.10: Antiderivatives The...

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