Lesson05b-_Strategies_for_Integration_ws - Worksheet for Section 6.13 Strategies for Integration MATH-UA 122.006 Calculus II Spring 2012 Summary of

Lesson05b-_Strategies_for_Integration_ws - Worksheet for...

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Worksheet for Section 6.1–3 Strategies for Integration MATH-UA 122.006: Calculus II Spring 2012 Summary of Integration Techniques Step 1. Simplify the integrand if possible, and use procedural rules to break down the integral (dis- tribute across sums, pull out constants, etc.) Step 2. Use the basic formulas like Formulas 1–20 in your table of integrals on reference page 6 (back pages). These are worth memorizing. Step 3. Make any substitution that will transform the integral into a simpler one. Step 4. Classify the integrand by “form”: I. Integration by parts. A. Polynomials are a good choice of u because they get simpler when differentiating. B. Inverse functions like ln, arcsin, arctan are also a good choice of u because they get simpler when differentiating. C. Remember also that the product of an exponential and a sine or cosine can be integrated by parts twice. II. Trigonometric forms: A. sin m x cos n x dx : If m is odd, save sin x dx and let u = cos x .

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