Trigonometric Substitution Notes

Trigonometric Substitution Notes - Trigonometric...

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Unformatted text preview: Trigonometric Substitution (Section 7.3) Brief Trigonometry Review: Reference Triangles: sin = sec = cos = csc = tan = cot = Example 0.1. If cos = x 4 , find the values of the remaining 5 trig functions. Trigonometric Substitution Used for integrals of the form: R dx ( a 2 + x 2 ) m R dx ( a 2- x 2 ) m R dx ( x 2- a 2 ) m R a 2 + x 2 dx R a 2- x 2 dx R x 2- a 2 dx Use the following substitutions: Expression Substitution Identity a 2- x 2 x = a sin 1- sin 2 = cos 2 a 2 + x 2 x = a tan 1 + tan 2 = sec 2 x 2- a 2 x = a sec sec 2 - 1 = tan 2 Example 0.2. Using trig substitution for indefinite integrals: Evaluate Z dx 9 + x 2 1. Determine which of the above substitutions to use. 2. Find dx . 3. Integrate in terms of using whatever method is appropriate. 4. Use a reference triangle to replace trig functions with expressions in terms of x . Example 0.3. Evaluate Z x 2 4- x 2 dx Example 0.4. Trigonometric Substitution for Definite Integrals:Example 0....
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Trigonometric Substitution Notes - Trigonometric...

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