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Midterm

2007 Test 3 solution

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Department
Mathematics
Course
MAT137Y1
Professor
N/ A
Semester
Winter

Description
MAT137Y20072008WinterSessionSolutionstoTermTest31EvaluatethefollowingintegralsandsimplifyyouranswerZ3x1dx8i2xZZ323111x3x3x12dxx3dxx3x3lnjxjC22xxx2xZ2xe8iidx4x1e2x2xLetueThendu2edxandwehaveZ111du2xarctanuarctaneC221u22Z2x10iiidx322x642Bytrigonometricsubstitutionletx8tanqsodx8secqdqThisgivesusZZZ22264tanqtanqsecq128secqdqdqdq338secqsecqsecqZsecqcosqdqlnjsecqtanqjsinqCp2xxx64pCln288x64px2plnjx64xjC2x64Z210ivlnx9dx2x2LetIbetheintegralBypartsweletulnx9dvdxsodudxand2x9vxThusZZ22x922Ixlnx9dxxlnx921dx22x9x9ZZdxAB22xlnx92x18xlnx92x18dxx3x3x3x311UsingpartialfractionswegetAandBTherefore66Z332dxIxlnx92xx3x32xlnx92x3lnjx3j3lnjx3jC1
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