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Greg Kelly, Hanford High School, Richland, Washington

Photo by Vickie Kelly, 2004. Greg Kelly, Hanford High School, Richland, Washington. Ch.8 Extra Topic:. Trigonometric Substitutions. Monticello (Thomas Jefferson’s home), Alexandria, VA. 1. These are in the same form.

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Greg Kelly, Hanford High School, Richland, Washington

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  1. Photo by Vickie Kelly, 2004 Greg Kelly, Hanford High School, Richland, Washington Ch.8 Extra Topic: Trigonometric Substitutions Monticello (Thomas Jefferson’s home), Alexandria, VA

  2. 1 These are in the same form. We can use right triangles and the pythagorean theorem to simplify some problems.

  3. 1 We can use right triangles and the pythagorean theorem to simplify some problems. This is a constant.

  4. If the integral contains , we use the triangle at right. If we need , we move a to the hypotenuse. If we need , we move x to the hypotenuse. This method is called Trigonometric Substitution.

  5. 2 double angle formula

  6. 2 double angle formula

  7. We can get into the necessary form by completing the square. 5

  8. 6 Complete the square:

  9. Here are a couple of shortcuts that are result from Trigonometric Substitution: These are on your list of formulas. They are not really new. p

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