Results 1 to 2 of 2

Math Help - Sorry Guys - One last Improper Integration question (e^x)/ ((e^x) -1) Why Divergent??

  1. #1
    Junior Member
    Joined
    Aug 2012
    From
    Maryland
    Posts
    45

    Sorry Guys - One last Improper Integration question (e^x)/ ((e^x) -1) Why Divergent??

    Sorry. I'm coming to the end of my four hour review. I try not to disturb you guys too much but I guess I'm just brain dead now.

    So the problem is the integral of (e^x) / ((e^x) -1) from -1 to 1

    I wasn't sure what to do at first so I made it

    (e^x) -1) +1 / ((e^x) -1)

    so that I could split the integral into

    (e^x -1)/(e^x-1) and get x
    and then

    1 / ((e^x) - 1)

    And then I just solved it straightup. I won't show that because it's obviously completely wrong if it's divergent.

    How exactly is this done. Sorry to disturb you guys again and thank you * 1000000 + Lim x-> inifinity of x^2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,888
    Thanks
    682

    Re: Sorry Guys - One last Improper Integration question (e^x)/ ((e^x) -1) Why Diverge

    if part of the definite integral diverges, it all diverges ...

    \lim_{a \to 0^+} \int_a^1 \frac{e^{x}}{e^x - 1} \, dx

    \lim_{a \to 0^+} \left[\ln(e^x - 1) \right]_a^1

    \lim_{a \to 0^+} \left[\ln(e - 1) - \ln(e^a - 1) \right]

    \lim_{a \to 0^+} \ln \left(\frac{e - 1}{e^a - 1}\right) = \infty
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Improper integral convergent or divergent?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 5th 2010, 12:47 PM
  2. Improper integral. Convergent or divergent?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 2nd 2010, 06:20 AM
  3. Divergent Improper Integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 18th 2010, 06:21 PM
  4. Proving an improper integral divergent.
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 7th 2010, 12:11 AM
  5. convergent and divergent improper integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 8th 2009, 09:15 AM

Search Tags


/mathhelpforum @mathhelpforum