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Inverse Trigonometric Functions: Integration

Inverse Trigonometric Functions: Integration. Lesson 5.8. Review. Recall derivatives of inverse trig functions. Integrals Using Same Relationships. When given integral problems, look for these patterns. Identifying Patterns.

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Inverse Trigonometric Functions: Integration

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  1. Inverse Trigonometric Functions: Integration Lesson 5.8

  2. Review Recall derivatives of inverse trig functions

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

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

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

  6. Simplify.

  7. The hardest part is getting the integral into the proper form.

  8. The hardest part is getting the integral into the proper form.

  9. The hardest part is getting the integral into the proper form.

  10. The hardest part is getting the integral into the proper form.

  11. The hardest part is getting the integral into the proper form.

  12. Simplify.

  13. Simplify.

  14. Simplify.

  15. Simplify.

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

  17. 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

  18. Example COMPLETE THE SQUARE!!!!

  19. 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

  20. Basic Integration Rules Note table of basic rules 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

  21. 2. Find the area of the region bounded by

  22. 2. Find the area of the region bounded by

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