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MATH 231 -
exam1_sample_problems_FA13
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Math 231, AL1, AL2, AL3: Sample Problems from old Calculus II exams.These questions are sample exam problems from previous years. This is not a comprehensivelist. This is not a complete study guide.1. Evaluate the following integrals.a)Zln xx2dxb)Zx3√x2− 9dx (Be sure you can do this using a trig substitution. It is also possible to do witha u-substitution)c)Zx + 2x3+ xdxd)Zdx√4x2− 4x + 5e)Zarctan x dxf)Zπ0x sin2(x)dxg)Ze1dxx(x2+ 1)h)Zsec2(x) tan2(x)dxi)Zdxx(x2− 1)32j)Z32dxx(x − 1)k)Z√1 + ln xx ln xdx2. Determine whether each improper integral converges or diverges.a)Z∞213√xdxb)Z∞21√x + 2dxc)Z∞1exx100dxd)Z∞1x3+ x + 1x4+ 2x + 2dxe)Z∞1x2+ x + 1x5+ 2x + 2dxf)Z101√xdxg)Z∞1e−x(x5+ 2x + 2)
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