Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Improper integral convergence or divergence.

  1. Feb 10, 2010 #1
    1. The problem statement, all variables and given/known data

    Use Comparison Theorem to determine whether the integral is convergent or divergent:

    integral from 0 to infinity of: arctan(x) / (2 + e^x)

    Should look like this: http://bit.ly/cAhytV [Broken]

    2. Relevant equations


    3. The attempt at a solution

    I tried to compare this with the integral from 0 to infinity of 1/e^x, but that didnt succeed since 1/e^x converges and the given function is less than 1/e^x. I am not sure what to compare this with
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 10, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Not sure why you chose 1/ex since [itex]\arctan x \le \pi/2[/itex] but not bounded by 1.

    Anyway, why wouldn't you have succeeded if your integral is less than a known convergent integral? Your problem would be if your unknown integral was greater than a known convergent integral.
    Last edited by a moderator: May 4, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook