Trigonometric substitutions
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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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Trigonometric substitutions

Trigonometric Substitutions

A topic you should see before you leave me…


Trigonometric substitutions

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…


Trigonometric substitutions

How?

  • Using right triangles…


Trigonometric substitutions

How?

  • Using right triangles…


Trigonometric substitutions

How?

  • Using right triangles…


Procedure

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.


Example 1

Example 1


Example 2

Example 2


Example 3

Example 3


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