Calculus II (MAT 146) Dr. Day Friday August 30, 2013 - PowerPoint PPT Presentation

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Calculus II (MAT 146) Dr. Day Friday August 30, 2013

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Calculus II (MAT 146) Dr. Day Friday August 30, 2013
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Calculus II (MAT 146) Dr. Day Friday August 30, 2013

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  1. Calculus II (MAT 146)Dr. Day Friday August 30, 2013 • Questions: Integral Apps • Finish Volume Calculations and Applications (6.2) • Begin Chapter 7: More Methods of Integration • 7.1 Integration by Parts MAT 146

  2. Review: Integral Apps (1) Calculate the exact value of the area between the curves f(x) = x3 – x2 – 2x + 1 and g(x) = x2 – 2x + 1. Show calculus and algebraic evidence for all aspects of your solution process. (2) Determine the average value of f(x) = sin(x) on the interval [0,π]. How many values ckexist, on [0,π], such that f(ck) generates that average value? Provide evidence for your responses. MAT 146

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  7. Volumes of Solids of Revolution (6.2 & 6.3) • Dynamic Illustration #1 (discs) • Dynamic Illustration #2 (washer) • Dynamic Illustration #3 (shell) • Dynamic Illustration #4 (cross section I) (cross section II) MAT 146

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  9. Undoing the Product Rule MAT 146

  10. Integration by Parts • An Integral with a Product Integrand • Examples MAT 146

  11. Integration by Parts • Key Component of Integrand’s Two Factors • For at least one factor, its derivative is “simpler” than the factor. • For at least one factor, its anti-derivative is no more complex than the factor. MAT 146

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  13. You Choosing U: A Decision Algorithm L: log functions I: inverse trig functions A: algebraic functions T: trig functions E: exponential functions MAT 146

  14. Assignments WebAssign • 6.2 Homework due Tuesday at midnight • Calc I Review: WA Tasks due Sunday and Tuesday • 7.1 (IBP) Test #1: Thursday/Friday Sept 12-13 MAT 146