Unit: Techniques of Integration Module: Introduction to Trigonometric Substitution Trigonometric Substitutions on Rational Powers www.thinkwell.com email@example.com 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
This is the end of the preview. Sign up
access the rest of the document.