Lesson 12 - Integration by miscellaneous substitution

# Lesson 12 - Integration by miscellaneous substitution -...

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TOPIC TECHNIQUES OF INTEGRATION

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TECHNIQUES OF INTEGRATION 1. Integration by parts 2. Integration by trigonometric substitution 3. Integration by miscellaneous substitution 4. Integration by partial fraction
TECHNIQUES OF INTEGRATION 3. Integration by miscellaneous substitution

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OBJECTIVES OBJECTIVES translate a rational function of sine and cosine into a rational function of another variable; use the basic identities in evaluating integrals involving rational functions of sine and cosine; and evaluate the given integrals using appropriate substitutions.
Integration by miscellaneous substitution : A. Integration of rational functions of sine and cosine using half angle substitution In this lesson we shall introduce several substitution method to simplify the form of the integrand. They are as follows: B. Fractional powers of x D. Reciprocal substitution C. Algebraic substitution

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sine and cosine Half-Angle Substitution sin x cos x z If an integrand is a rational function of
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## This note was uploaded on 10/19/2011 for the course MATH 22 taught by Professor Ma'amzapanta during the Fall '11 term at Mapúa Institute of Technology.

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Lesson 12 - Integration by miscellaneous substitution -...

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