Calculus II Notes 8.5 - Calculus II-Stewart Dr. Berg Spring...

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Calculus II- Stewart Dr. Berg Spring 2010 Page 1 8.5 8.5 Integration Strategy Integration is more difficult than differentiation. We need a strategy. First, learn the basic integrals. These are summarized in a table at the beginning of the section in the book. Strategy 1) Simplify. e.g. x 1 + x ( ) dx = x + x dx 2) Try a simple substitution. e.g. For x x 2 1 dx try u = x 2 1 . 3) Classify by form. a) Trigonometric: products of sine and cosine, tangent and secant, or cotangent and cosecant require the procedures examined in 8.2. b) Rational: use the method of partial fractions in 8.4. c) Integration by Parts: a product of a polynomial and a transcendental function may need the techniques of 8.1. d) Radicals: i) x 2 ± a 2 requires a trigonometric substitution. ii) ax + b n requires the rationalizing substitution u = ax + b n . 4) Try again! Exercise 1 Evaluate tan 3 x dx
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This note was uploaded on 04/04/2011 for the course MATH 408 L taught by Professor Zheng during the Spring '10 term at University of Texas at Austin.

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Calculus II Notes 8.5 - Calculus II-Stewart Dr. Berg Spring...

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