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# 6.1__summer - 6.1 Antiderivatives A function F is an...

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6.1 Antiderivatives A function F is an antiderivative of f on an interval I if F’(x) = f (x) for all x in I . Theorem: Let G be an antiderivative of a function f. Then, every antiderivative F of f must be of the form F(x) = G(x) + C where C is a constant. Basic Integration Rules RULES 1.∫ k dx = kx + C 2.∫ x n dx = x n+1 n + 1 where n≠ -1 3.∫ c f(x) dx = c ∫ f(x) dx where c is a constant 4.∫ [ f(x) + g(x)] dx = ∫ f(x) dx + ∫ g(x) dx 5.∫ [ f(x) - g(x)] dx = ∫ f(x) dx - ∫ g(x) dx Find the indefinite integral ∫ 4 dx

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Find the indefinite integral ∫ x 3 dx Find the indefinite integral ∫ 7x 5 dx Find the indefinite integral ∫ (7x 5 - 2x 3 + x – 8) dx Find the indefinite integral ∫ (t 5/2 – 2t 1/2 + 6t -1/2 – 8) dx
Lorimar Watch Company manufactures travel clocks. The daily marginal cost function associated with producing these

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## This note was uploaded on 10/07/2011 for the course MATH 1431 taught by Professor Vaughn during the Spring '08 term at LSU.

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6.1__summer - 6.1 Antiderivatives A function F is an...

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