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Trigonometric Substitutions

Trigonometric Substitutions. A topic you should see before you leave me…. Why?. Allows you to evaluate integrals involving Oh you meant why am I making you do this? It is part of the curriculum for all Calc II classes in college…. How?. Using right triangles…. How?.

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Trigonometric Substitutions

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  1. Trigonometric Substitutions A topic you should see before you leave me…

  2. Why? • Allows you to evaluate integrals involving • Oh you meant why am I making you do this? It is part of the curriculum for all Calc II classes in college…

  3. How? • Using right triangles…

  4. How? • Using right triangles…

  5. How? • Using right triangles…

  6. Procedure • Write down the substitution for x, calculate dx, and specify the selected values of for the substitution. • Make the substitution into the integrand and simplify algebraically. • Integrate the trig integral keeping in mind the restrictions on the angle . • Draw an appropriate reference triangle to reverse the substitution in the integration result and convert back to the original variable x.

  7. Example 1

  8. Example 2

  9. Example 3

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