Chapter 28 Math 270

Chapter 28 Math 270 - Chapter 28: Methods of Integration...

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Chapter 28: Methods of Integration Sec 7: Integration by Parts There are many methods of transforming integrals into forms that can be integrated by one of th basic formulas. Since the derivative of a product of functions is found by use of the formula The differential of a product of functions is given by . Integrating both sides of this equation, we have. Solving for , we obtain Example 1 Integrate: Integral doesn’t fit any of previous forms we discussed. Neither x nor sin x can be made a factor of a proper du. However, by choosing u = x and dv = sin x dx, integration by parts can be used. Finding the differential of u and integrating dv, we find du and v. this gives us Now we substitute to Eq. 1 Example 2: Integrate
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Form doesn’t fit general power rule, for x dx is not factor of differential of 1 – x. Choosing u = x and , we have and v can readily be determined. Substitute to Eq. 1 This point, see we can complete integration. 1.
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Chapter 28 Math 270 - Chapter 28: Methods of Integration...

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