Lesson26_-_Integration_by_Substitution_ws

Lesson26_Integrati - 1 Sometimes there is more than one way to skin a cat 8 Find Z x 1 x dx both by long division and by substituting u = 1 x 9

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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 2. Z 4 0 x p x 2 + 9 dx , u = x 2 + 9 3. Z e x x dx , u = x . 4. Z cos 3 xdx 5 + 2 sin 3 x , u = 5 + 2 sin 3 x In these problems, you need to determine the substitution yourself. 5. Z (4 - 3 x ) 7 dx . 6. Z π/ 3 π/ 4 csc 2 (5 x ) dx 7. Z x 2 e 3 x 3 - 1 dx
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Unformatted text preview: 1 Sometimes there is more than one way to skin a cat: 8. Find Z x 1 + x dx , both by long division and by substituting u = 1 + x . 9. Find Z 2 z dz 3 √ z 2 + 1 , both by substituting u = z 2 + 1 and u = 3 p z 2 + 1. Use the trigonometric identity cos 2 α = cos 2 α-sin 2 α = 2 cos 2 α-1 = 1-2 sin 2 α to find 10. Z sin 2 xdx 11. Z cos 2 xdx ‘ 12. Find Z sec xdx by multiplying the numerator and denominator by sec x + tan x . 2...
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This note was uploaded on 07/19/2010 for the course MATHEMATIC V63.0121 taught by Professor Leingang during the Spring '09 term at NYU.

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Lesson26_Integrati - 1 Sometimes there is more than one way to skin a cat 8 Find Z x 1 x dx both by long division and by substituting u = 1 x 9

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