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5.7 Inverse Trigonometric Functions: Integration

5.7 Inverse Trigonometric Functions: Integration. Review. 2. Recall derivatives of inverse trig functions. Integrals Using Same Relationships. When given integral problems, look for these patterns. 3. Identifying Patterns. 4.

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5.7 Inverse Trigonometric Functions: Integration

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  1. 5.7 Inverse Trigonometric Functions: Integration

  2. Review 2 Recall derivatives of inverse trig functions

  3. Integrals Using Same Relationships When given integral problems, look for these patterns 3

  4. Identifying Patterns 4 For each of the integrals below, which inverse trig function is involved?

  5. Warning If they are not, how are they integrated? 5 Many integrals look like the inverse trig forms Which of the following are of the inverse trig forms?

  6. Try These 6 Look for the pattern or how the expression can be manipulated into one of the patterns

  7. Completing the Square • Often a good strategy when quadratic functions are involved in the integration • Remember … we seek (x – b)2 + c • Which might give us an integral resulting in the arctan function

  8. Completing the Square Try these

  9. Rewriting as Sum of Two Quotients • The integral may not appear to fit basic integration formulas • May be possible to split the integrand into two portions, each more easily handled

  10. Basic Integration Rules • Note table of basic rules • Page 364 • Most of these should be committed to memory • Note that to apply these, you must create the proper du to correspond to the u in the formula

  11. Assignment 11 Lesson 5.7 Page xxx Exercises

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