Integral Final.pdf - 1 UNIVERSITY OF WINDSOR DEPARTMENT OF MATHEMATICS AND STATISTICS Integral Calculus 62-141-01 Final Exam Friday Last name(PRINT

Integral Final.pdf - 1 UNIVERSITY OF WINDSOR DEPARTMENT OF...

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1 UNIVERSITY OF WINDSOR DEPARTMENT OF MATHEMATICS AND STATISTICS Integral Calculus 62-141-01 Final Exam Friday, August 22, 2014 Last 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 the grade table page(the last page). You have 180 minutes. Read carefully and answer all questions. Show all the work. No calculators, cell phones or other electronic devices are allowed. Work all problems in the space provided. You must give exact answers (and not decimal approximations). Do not detach any pages.
2 1.(26)Evaluate the following integrals.(a)Z(lnx)2dx.(b)Zsin3xcos10xdx.(c)Zsin-1xcos-1x1-x2dx
3 (d) Z 16 - x 2 x 2 dx . (e) Z sin 2 x 1 + sin 4 x dx
4 2.(7)Show thatZcosnxdx=1ncosn-1xsinx+n-1nZcosn-2xdx3.(14)Evaluate the integrals. (a) Z 0 -∞ x 2 e x 3 dx (b) Z 1 - 1 e x 4 sin x 5 + x 2 + x 4 dx
5 (c) Z 1 0 ln x x dx 4. (5) Find the length of the curve y = x 6 12 + 1 8 x 4 , 1 x 2
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