Lesson26_-_Integration_by_Substitution_ws-sol

Lesson26_-_Integration_by_Substitution_ws-sol - Solutions...

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Unformatted text preview: Solutions to Worksheet for Section 5.5 Integration by Substitution V63.0121, Calculus I Spring 2010 Find the following integrals. In the case of an indefinite integral, your answer should be the most general antiderivative. In the case of a definite integral, your answer should be a number. In these problems, a substitution is given. 1. Z (3 x- 5) 17 dx , u = 3 x- 5 Solution. As suggested, we let u = 3 x- 5. Then du = 3 dx so dx = 1 3 du . Thus Z (3 x- 5) 17 dx = 1 3 Z u 17 du = 1 3 1 18 u 18 + C = 1 54 (3 x- 5) 18 + C 2. Z 4 x p x 2 + 9 dx , u = x 2 + 9 Solution. We have du = 2 xdx , which takes care of the x and dx that appear in the integrand. The limits are changed to u (0) = 9 and u (4) = 25. Thus Z 4 x p x 2 + 9 dx = 1 2 Z 25 9 udu = 1 2 2 3 u 3 / 2 25 9 = 1 3 (125- 27) = 98 3 . 3. Z e x x dx , u = x . 1 Solution. We have du = 1 2 x dx , which means that Z e x x dx = 2 Z e u du = 2 e u + C 4....
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Lesson26_-_Integration_by_Substitution_ws-sol - Solutions...

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