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Homework Help: Improper integrals

  1. May 3, 2013 #1
    1. The problem statement, all variables and given/known data
    Check if the following integrals diverge:
    Int(1/(x^3-2x^2+x), from 0 to 1) and Int(1/(x^3+x^2-2x)

    2. Relevant equations
    Ratio-test(not sure if thats the name)

    3. The attempt at a solution
    I have solved the problem and found that both integrals diverge at x=0. I just want to check if you guys agree with me.
  2. jcsd
  3. May 3, 2013 #2
    Ratio test is for infinite series, not a improper integrals. It would be helpful to see your work.
  4. May 3, 2013 #3


    Staff: Mentor

    Both integrands are undefined at x = 0, which is why the integrals are improper. Both integrands are also undefined at the other endpoint, x = 1.

    You need to use limits to evaluate these integrals - then you can decide whether either one diverges.
  5. May 4, 2013 #4
    Okay ratio test was then not the correct name. What I did was use the test that if limx->0[g/f>0] then g also diverges if f diverges. So I took f as 1/x^3. Isn't this correct, and dont you guys get that both integrals diverge?
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