6.2_Integration_by_Substitution_summer

6.2_Integration_by_Substitution_summer - Replace u by g(x)...

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6.2 Integration by Substitution Warm-u[s from 6.1 Find the indefinite integral f(x) = ∫ (16x 3 + 5x – 7) dx Find an antiderivative: f(x) = 16/(23x) Find the indefinite integral f(x) = ∫ 16e x dx Find f(x) by solving the initial value problem f ‘(x) = 6 + e x and f(1) = 7 + e Canon Precision Instruments makes an automatic electronic flash. The estimated marginal profit associated with producing
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and selling these flashes is -0.006x + 30 dollars/unit/month when the production level is x units per month. Cannon’s fixed costs for these flashes is $17,000/month. What is the maximum monthly profit? 6.2 Integration by Substitution Let u = g(x) where g(x) is a part of the integrand, usually the “inside” function Find du which equals g’(x) dx Convert the entire integral into one containing only u and du by substitution Evaluate the resulting integral
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Unformatted text preview: Replace u by g(x) to find the final solution as a function of x. Find the indefinite integral: (3x 2- 2x +1)(x 3- x 2 + x) 13 dx Find the indefinite integral: 2(11x+ 9) 5 dx Find the indefinite integral: x 6 (7x 7 + 3) 4 dx Find the indefinite integral: 8t 7 (t 8 + 5) (1/4) dt Find the function f given that the slope of the tangent line to the graph at any point (x, f(x) is f (x) and that the graph passes through (2,1) where f (x) = 3x 2 /(2 x 3- 7) Find the indefinite integral: ___5x 2 ___ dx (9 4x 3 ) Find the indefinite integral: e 8x dx Find the indefinite integral: ___e 6x ___ dx (3 + e 6x ) Find the indefinite integral: 3x 4 e (x^5 8) dx Find the indefinite integral: (ln x) 20 / x dx Find the indefinite integral: 12/[x(ln (x)) (38) ] dx...
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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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6.2_Integration_by_Substitution_summer - Replace u by g(x)...

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