Unit: Techniques of Integration Module: Trigonometric Substitution Strategy An Overview of Trig Sub Strategy www.thinkwell.com firstname.lastname@example.org Copyright 2001, Thinkwell Corp. All Rights Reserved. 1579 –rev 06/14/2001 • 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 function into the integrand. 3. Evaluate the resulting simpler integral. 4. Convert from trigonometric functions back to the original variables. When you notice a radical expression or a rational power in an integrand, then the integral is a good candidate for trigonometric substitution . The fact that the square root of the difference must correspond to the leg of the right triangle follows from the Pythagorean theorem. The square root of the sum of the squares is equal to the length of the hypotenuse, so to get the radical expression to fit
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