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!

Determining when an integral converges or diverges

  1. Jul 10, 2009 #1
    1. The problem statement, all variables and given/known data
    determine whether the integral converges or diverges:
    [tex]\int_0^1\!\sqrt{\frac{(1+x)}{(1-x)}}dx[/tex]

    2. Relevant equations

    I know what if the value is a finite number, it converges, otherwise it diverges. Teacher was was able to determine the fact just by looking at it... what is the procedure for this?
     
  2. jcsd
  3. Jul 10, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You look near the point where the integrand is singular, in this case near x=1. The numerator is ~2 and the denominator (1-x)=y is near zero. So the integral is going to have the same convergence properties as the integral of 1/sqrt(y) around zero. It converges.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook