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7.2 Integration By Parts

Photo by Vickie Kelly, 1993. Greg Kelly, Hanford High School, Richland, Washington. 7.2 Integration By Parts. Badlands, South Dakota. Objectives. Find the antiderivative using integration by parts. Use a tabular method to perform integration by parts. Graphing Calculator Activity:.

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7.2 Integration By Parts

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  1. Photo by Vickie Kelly, 1993 Greg Kelly, Hanford High School, Richland, Washington 7.2 Integration By Parts Badlands, South Dakota

  2. Objectives • Find the antiderivative using integration by parts. • Use a tabular method to perform integration by parts.

  3. Graphing Calculator Activity: Graph and find the area bounded by and Window: xmin=-1.88 ymin=-1.2 xmax=1.88 ymax=1.7 A valentine for your sweetie "pi". fnInt(y2-y1,x,-1,1) Shade(y1,y2) {Draw 7}

  4. How do you integrate

  5. 7.2 Integration By Parts Start with the product rule: This is the Integration by Parts formula.

  6. Logs, Inverse trig, Algebraic, Trig ,Exponential dv is easy to integrate. u differentiates to zero (usually). The Integration by Parts formula is a “product rule” for integration. Choose u in this order: LIATE

  7. LIATE

  8. LIATE

  9. Can't integrate arcsin!

  10. Example 1: LIATE polynomial factor

  11. This is still a product, so we need to use integration by parts again.

  12. A Shortcut: Tabular Integration (Tic-Tac-Toe Method) Tabular integration works for integrals of the form: where: Differentiates to zero in several steps. Integrates repeatedly.

  13. Compare this with the same problem done the other way:

  14. Example 5: This is easier and quicker to do with tabular integration!

  15. Homework Handout #1-15 odd 21, 29, 31, 35 p

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