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Unformatted text preview: Section 5.5: The Substitution Rule For indefinite integrals of the form f g x ( 29 ( 29 g x ( 29 dx , let u = g x ( 29 . Then du = g x ( 29 dx , and the original integral can be expressed as f u ( 29 du . Choose u = g x ( 29 such that its derivative also appears in the original integral, except perhaps for a constant. In other words, follow these steps: (1) make the substitution u = g x ( 29 ; (2) determine du = g x ( 29 dx ; (3) write the integral in terms of u ; (4) integrate in terms of u ; (5) back substitute to return to variable x . For definite integrals of the form f g x ( 29 ( 29 g x ( 29 a b dx , again let u = g x ( 29 . Then du = g x ( 29 dx , u lower = g a ( 29 , u upper = g b ( 29 , and the original integral can be expressed as f u ( 29 u lower u upper du . In other words, follow these steps: (1) make the substitution u = g x ( 29 ; (2) determine du = g x ( 29 dx ; (3) change the limits of integration to be valid for u , where u lower...
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This note was uploaded on 01/12/2010 for the course MATH 44245 taught by Professor Famiglietti during the Fall '07 term at UC Irvine.
 Fall '07
 FAMIGLIETTI
 Math, Definite Integrals, Derivative, Integrals

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