1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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