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14209an6.4-6 - Let’s look again at Z e x 3-1 3 x 2 dx...

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c Kendra Kilmer April 2, 2009 Section 6.2 - Integration by Substitution Recall that d dx ( f [ g ( x )]) = Thus, Example 1: What is Z e x 3 - 1 · 3 x 2 dx ? General Indefinite Integral Formulas 1. Z e f ( x ) f 0 ( x ) dx = 2. Z [ f ( x )] n f 0 ( x ) dx = 3. Z 1 f ( x ) f 0 ( x ) dx = Integration by u-Substitution 1. Select u (look for function where you normally have x ) 2. Take the derivative of u using du dx notation. 3. Bring dx to the right hand side. 4. Bring any constant multiples to the left-hand side. 5. Substitute to replace all terms with x ’s. 6. Integrate with u ’s. 7. Return x ’s into the problem. 4
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c Kendra Kilmer April 2, 2009
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Unformatted text preview: Let’s look again at Z e x 3-1 · 3 x 2 dx Example 3: Evaluate the following: a) Z 7 ( 8 x + 3 ) 10 dx b) Z 2 x 2 4 p x 3 + 2 dx c) Z 3 ( x 3 + 1 ) ( 3 x 4 + 12 x ) 7 dx d) Z 12 x 3 x 2 + 5 dx 5 c ± Kendra Kilmer April 2, 2009 e) Z x 5 √ 7 x 2 + 11 dx f) Z ( 2 x 6 e x 7 + 1 ) dx g) Z e x-e-x e x + e-x dx h) Z x √ x + 2 dx i) Z x ( x 5 + 1 ) 2 dx Section 6.2 Homework Problems: 1,7,13,19,25,31,37,49,55,61,69 and supplemental problems 6...
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