227-04Quiz2SolutionsSp11

227-04Quiz2SolutionsSp11 - x dx = 1 3 xe 3 x &...

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Math 227.04 Quiz 2 February 10, 2011 Name___________________________Key____________ Instructions. Calculators are not permitted. For full credit, you must show your work and write complete mathematical sentences. Please display your answers clearly and erase or cross out any work you wish to be ignored. 1. Find Z xe 3 x dx: Solution. Let u = x; du = dx , and dv = e 3 x dx; v = 1 3 e 3 x : Then Z xe 3 x dx = 1 3 xe 3 x Z 1 3 e 3
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Unformatted text preview: x dx = 1 3 xe 3 x & 1 9 e 3 x + C: 2. Find Z 2 1 ln x dx: Express your answer in exact form (not as a decimal expression). Solution. Let u = ln x; du = 1 x dx; and dv = dx , v = x: Then Z 2 1 ln x dx = x ln x j 2 1 & Z 2 1 x 1 x dx = (2 ln 2 & ln 1) & Z 2 1 1 dx = 2 ln 2 & ( x j 2 1 ) = 2 ln 2 & (2 & 1) = (2 ln 2) & 1 : 1...
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