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1UNIVERSITY OF WINDSORDEPARTMENT OF MATHEMATICS AND STATISTICSIntegral Calculus 62-141-01Final ExamFriday, August 22, 2014Last name(PRINT):First name:Student No.:Section No.:Instructions:•This test has 12 problems and a total of 13 pages, including this cover page and thegrade table page(the last page). You have 180 minutes.•Read carefully and answerallquestions. Show all the work.•No calculators, cell phones or other electronic devices are allowed.•Work all problems in the space provided.•You must giveexactanswers (and not decimal approximations).•Do not detach any pages.
21.(26)Evaluate the following integrals.(a)Z(lnx)2dx.(b)Zsin3xcos10xdx.(c)Zsin-1xcos-1x√1-x2dx
3(d)Z√16-x2x2dx.(e)Zsin 2x1 + sin4xdx
42.(7)Show thatZcosnxdx=1ncosn-1xsinx+n-1nZcosn-2xdx3.(14)Evaluate the integrals.(a)Z0-∞x2ex3dx(b)Z1-1ex4sinx5 +x2+x4dx
5(c)Z10lnx√xdx4.(5)Find the length of the curvey=x612+18x4, 1≤x≤2