227-04q3solnsSp2011

227-04q3solnsSp2011 - & 3 x 2 dx Solution x 2 x 2& 3...

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Math 227.04 Quiz 3 Solutions February 17, 2011 Name Instructions. Calculators are NOT allowed. You must show your work for full credit. Please display your answers clearly and erase or cross out any work you wish to be ignored. 1. (3 pts) Write out the form of the partial fraction decomposition for x 3 x 4 1 : Do not attempt to evaluate the undetermined coe¢ cients. Answer: x 3 x 4 1 = x 3 ( x 1) ( x + 1) ( x 2 + 1) = A x 1 + B x + 1 + Cx + D ( x 2 + 1) : 2. (7 pts) Find Z x + 2 x 2
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Unformatted text preview: & 3 x + 2 dx Solution: x + 2 x 2 & 3 x + 2 = x + 2 ( x & 1) ( x & 2) = A x & 1 + B x & 2 : Multiplying by ( x & 1) ( x & 2) yields x + 2 = A ( x & 2) + B ( x & 1) : Setting x = 1 ) 3 = & A ) 3 ) A = & 3 : Setting x = 2 ) 4 = B: Thus x + 2 x 2 & 3 x + 2 = & 3 x & 1 + 4 x & 2 so Z x + 2 x 2 & 3 x + 2 dx = Z ( & 3 x & 1 + 4 x & 2 ) dx = & 3 ln j x & 1 j + 4 ln j x & 2 j + C: 1...
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This note was uploaded on 10/16/2011 for the course MATH 227 taught by Professor Cheung during the Spring '09 term at S.F. State.

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