# Homework 13 Solution - Improper Integrals SUGGESTED...

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Improper IntegralsSUGGESTED REFERENCE MATERIAL:As you work through the problems listed below, you should reference Chapter 7.8 of the rec-ommended textbook (or the equivalent chapter in your alternative textbook/online resource)and your lecture notes.EXPECTED SKILLS:Given an improper integral, which either has an infinite interval of integration or aninfinite discontinuity, be able to evaluate it using a limit.Know how to determine if such an integral converges (and if so, what it converges to)or diverges.PRACTICE PROBLEMS:For problems 1-13, evaluate each improper integral or show that it diverges.1.Z11xdx2.Z3-∞3xx2+ 1dx-∞3.Z1e-xdx1e4.Z1xe-3x2dx16e-35.Z401x2/3dx3341
6.Z41(x-2)3dx187.Z621x-2dx48.Z2024-x2dxπ9.Z01x2+ 4x+ 5dx(Hint: Complete the square)π2-tan-1(2)10.Zπ20sinx3cosxdx3211.Zπ20tanxsec2x dx12.Z9013p(x-1)2dx913.Z101xlnxdx-∞

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