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Understanding Inverse Trig Functions in AP Calculus: Patterns and Generalizations

Learn to integrate inverse trig functions in AP Calculus by recognizing key patterns, generalizing derivative rules, and mastering techniques like substitution and completing the square. Remember to differentiate different functions, like arcsec and arcsin, noting their unique rules. Practice with examples and worksheets for better understanding.

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Understanding Inverse Trig Functions in AP Calculus: Patterns and Generalizations

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  1. 5014-Integration Inverse Trig AP Calculus

  2. Remember Patterns: 1 x y x y 1 x y 1

  3. Remember Derivaties:

  4. Generalize: Looks like arcsin pattern except NOT1 -

  5. MEMORIZE ! ais a constant. u = f (x)

  6. Examples: Straight Plug In

  7. Examples: Normal U - duProblem ? Inverse Trig. (also has a U-du component)

  8. Arctan vs. Ln Always check ln first!

  9. Example (introduce a variable factor): U - du ???? arcsec ???? REM:NEVER CROSS the with a variable ! ! !

  10. Example (introduce a variable factor): arcsec ???? U - du

  11. Examples (Complete the square):

  12. Examples (Complete the square): Negative lead

  13. Examples (Complete the square): Non-one lead

  14. Examples (THINK): ADD ZERO

  15. Last Update: • 02/06/06 • Assignment: Worksheet Larson 5.8

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