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Determine whether the integral is divergent. If convergent, evaluate.

  1. Feb 26, 2013 #1
    1. The problem statement, all variables and given/known data
    ∫ a= 2 b = ∞ (dv)/(v^2+7v-8)


    2. Relevant equations

    I have attempted the problem and am confused as to why the integral is not divergent.

    3. The attempt at a solution

    I integrated the function by using partial fractions and came up with a result of:
    -1/9ln(v+8)+1/9ln(v-1)

    I replaced 'b' limit of integration with 't' and solved for the limit of the function as 't' approaches infinity…
    lim t→∞ -1/9[ln(v+8)-ln(v-1)] with limits of integration, b =t and a = 2

    However when finding the limit, I realize that when substituting ∞ for 'v' I am left with the following result: -1/9[ln(∞+8)-ln(∞-1)]

    ln(∞) is equal to ∞, and ∞-∞ is equal to ∞. Therefore there is no limit for the function ∫ a= 2 b = ∞ (dv)/(v^2+7v-8) and it is divergent.

    This is not the case though, and the function convergent.

    Where is my mistake occurring?
     
  2. jcsd
  3. Feb 26, 2013 #2

    SammyS

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    Re: Determine whether the integral is divergent. If convergent, evalua

    A limit of the form ∞ - ∞ is indeterminate.

    You need to express it in a different way. use properties of logs to to get a more compact expression.
     
  4. Feb 26, 2013 #3
    Re: Determine whether the integral is divergent. If convergent, evalua

    ln(v+8)/ln(v+1) ?
    Would I then have to use L'hopitals rule?
     
  5. Feb 26, 2013 #4

    Dick

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    Re: Determine whether the integral is divergent. If convergent, evalua

    That's not a correct use of the rules of logs. Try again.
     
  6. Feb 26, 2013 #5

    SammyS

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    Re: Determine whether the integral is divergent. If convergent, evalua

    ln(a) - ln(b) = ln(a/b) .

    ln(a) - ln(b) ln(a)/ln(b) .
     
  7. Oct 16, 2017 #6
    Can some one help me figure out How ln( t+8)/(t-1) = 0
     
    Last edited: Oct 16, 2017
  8. Oct 16, 2017 #7

    Ray Vickson

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    If you mean
    $$ \frac{\ln (t+8)}{t-1}=0$$
    it is easy (figure out why). If you mean
    $$ \ln \left( \frac{t+8}{t-1} \right) = 0 $$
    you can spend a lifetime looking for a solution and never finding one. Why not?
     
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