CHAPTER 28 Methods of Integration Section 8 Integration by Trigonometric Substitution

CHAPTER 28 Methods of Integration Section 8 Integration by Trigonometric Substitution

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CHAPTER 28: Methods of Integration Section 8: Integration by Trigonometric Substitution Expression substitute identity 1. Integrate a) Let then so the proper substitution for x is b) To make substitution, first determine values of x^2 and dx. Use formula c) Substitute values and simplify d) Next substitute into radical using identity and simplify result e) Simplify further and use trigonometric identities. Fact 2. Evaluate a) We use the expression b) To evaluate use the substitution c) Then d) So use identities e) Original variable, x, must be reintroduced. Since which gives the following.
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Unformatted text preview: x ᵩ 3 f) The remaining side of the right triangle has length so g) Thus, = 3. Evaluate a) Write integrand contains form , try substitution a=2 b) To evaluate use substitution With c) Thus = d) To complete exercise, value of integral must be expressed in terms of original variable y. e) Initial substitution was y ᵩ 2 f) In diagram above, and g) So, 4. Evaluate a) To evaluate b) To complete exercise, the original variable, x, must be reintroduced. c) Use trigonometric identity 5. Evaluate...
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This note was uploaded on 01/09/2012 for the course ENG 1000c taught by Professor Balls during the Spring '10 term at DeVry Addison.

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CHAPTER 28 Methods of Integration Section 8 Integration by Trigonometric Substitution

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