Trigonometry Workbook For Dummies
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Before reading this article, you should check out the discussion of trig substitution in the companion article, “How to Use Trig Substitution to Integrate.”

With the trigonometric substitution method, you can do integrals containing radicals of the following forms:

This article concerns the first form which you tackle with the sine function. The other two forms are handled with the tangent and secant functions and are discussed in other articles.

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  1. Draw a right triangle where

    image1.png

    You should confirm this with the Pythagorean theorem.

    image2.png

the following figure shows a SohCahToa triangle.

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  1. Solve

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  2. then differentiate, and solve for dx.

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  3. Find which trig function equals the radical over the a (that’s the a from

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  4. not a as in adjacent), and then solve for the radical.

    Look at the triangle in the figure.

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  5. Use the results from Steps 2 and 3 to make substitutions in the original problem and then integrate.

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  6. The triangle shows that

    image9.png

    So substitute back for your final answer:

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It’s a walk in the park.

About This Article

This article is from the book:

About the book author:

Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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