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Unit: Techniques of Integration Module: Introduction to Trigonometric Substitution Using Trigonometric Substitution to Integrate Radicals www.thinkwell.com [email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved. Use trigonometric substitution to evaluate integrals involving the square root of the sum or difference of two squares. 1. Match the square root expression with the sides of a right triangle. 2. Substitute the corresponding trigonometric functions into the integrand. 3. Evaluate the resulting simpler integral. 4. Convert from trigonometric functions back to the original variables. In a difference of two squares under a radical, the positive term corresponds to the hypotenuse of a right triangle. Integrals that include radical expressions can be very tricky to evaluate. Consider this integral. Notice that there is no obvious u -substitution to make. Also notice that integration by parts will create successively more complicated integrals. The presence of a radical does empower you to
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This note was uploaded on 04/27/2010 for the course MATH 172 taught by Professor Hyon during the Spring '10 term at Community College of Denver.

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