Unit: Techniques of Integration Module: Introduction to Trigonometric Substitution Trigonometric Substitutions on Rational Powers 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 sum of two squares under a radical, the radical expression corresponds to the hypotenuse of the right triangle. Consider this integral. Notice that there is no obvious u-substitution that you can make and that other techniques of integration look unpromising. However, the expression in the denominator is
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