13112an5.12-15

13112an5.12-15 - c Kendra Kilmer March 1, 2012 Section 5.5...

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Unformatted text preview: c Kendra Kilmer March 1, 2012 Section 5.5 - The Substitution Rule Recall that d ( f [g(x)]) = dx Thus, Example 1: What is 3 −1 ex · 3x2 dx? General Indefinite Integral Formulas 1. e f (x) f ′ (x) dx = 2. [ f (x)]n f ′ (x) dx = 3. 1′ f (x) dx = f (x) 4. cos [ f (x)] f ′ (x) dx = Integration by u-Substitution 1. Select u (look for function where you normally have x) du notation. dx 3. Bring dx to the right hand side. 4. Bring any constant multiples to the left-hand side. 2. Take the derivative of u using 5. Substitute to replace all terms with x’s. 6. Integrate with u’s. 7. Return x’s into the problem. 12 c Kendra Kilmer March 1, 2012 Example 2: Let’s look again at 3 −1 ex · 3x2 dx Example 3: Evaluate the following: a) 7(8x + 3)10 dx b) 2x2 c) 3(x3 + 1) dx (3x4 + 12x)7 d) 12x dx 3x2 + 5 4 x3 + 2 dx 13 c Kendra Kilmer March 1, 2012 x e) √ 5 f) (2x6 ex g) ex − e−x dx ex + e−x h) √ i) x(x5 + 1)2 dx 7x2 + 11 7 +1 dx ) dx x dx x+2 14 c Kendra Kilmer March 1, 2012 2 j) (2x + 3)6 dx 0 √ π k) x cos(x2 ) dx 0 Example 4: An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t ) = 100e−0.01t liters per minute. How much oil leaks out during the first hour? Section 5.5 Highly Suggested Homework Problems: 1, 3, 5, 7, 9, 13, 15, 17, 19, 21, 23, 25, 29, 31, 41, 45, 47, 51, 53, 55, 63, 67 15 ...
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This note was uploaded on 04/01/2012 for the course MATH 131 taught by Professor Allen during the Fall '08 term at Texas A&M.

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13112an5.12-15 - c Kendra Kilmer March 1, 2012 Section 5.5...

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