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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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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

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1

These are in the same form.

We can use right triangles and the pythagorean theorem to simplify some problems.

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1

We can use right triangles and the pythagorean theorem to simplify some problems.

This is a constant.

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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.

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2

double angle formula

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2

double angle formula

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6

Complete the square:

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Here are a couple of shortcuts that are result from Trigonometric Substitution:

These are on your list of formulas. They are not really new.

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