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Improper Integral Check

  1. Mar 5, 2013 #1

    B18

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    Hi guys just want to check my answer for the following improper integral.
    ∫(2 to ∞) dv/v^2+2v-3. After doing partial fractions, integrating and evaluating I got the following for the answer: 0-(1/4)ln(1/5)=(1/4)ln(1/5)
    How does this compare to other answers?
    Is there a way I can accurately check this answer myself?
     
  2. jcsd
  3. Mar 5, 2013 #2

    HallsofIvy

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    1) How are you handling the limits at infinity?

    2) Certainly, -(1/4)ln(1/5) is not equal to (1/4)ln(1/5)!
     
  4. Mar 5, 2013 #3

    B18

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    I made the natural logs into a quotient by log rules and evaluated that for t approaching infinity. I do agree with you my answer should have been negative.
     
  5. Mar 6, 2013 #4

    HallsofIvy

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    That's not what I get. After integrating and recombining the logarithms, I get -(1/4)ln(3) at infinity.
     
  6. Mar 6, 2013 #5

    B18

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    I'm not sure how you got ln of 3 before evaluating I have lim t-> infinity 1/4ln(v-1/v+3) evaluated from 2 to t.
    Lim t->infinity [1/4ln((t-1)/(t+3))-1/4ln((2-1)/2+3))
    Giving me -1/4ln(1/5)
     
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