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: A tricky integral

  1. Jan 14, 2009 #1
    1. The problem statement, all variables and given/known data
    I should find this integral:
    [tex]\int[/tex]b x(1/[tex]\Pi[/tex])(1/(1+x2)dx

    2. Relevant equations

    [tex]\int[/tex]1/(1+x2)dx = arctan(x)

    3. The attempt at a solution
    The Only thing I've succeeded in doing is to take the 1/[tex]\Pi[/tex] and put it in front of the integral like this:
    (1/[tex]\Pi[/tex])[tex]\int[/tex]b (x/(1+x2)dx
    And I know that the integral of 1/(1+x2) equals arctan(x) but how could that help me? Ive tried to use the equation
    [tex]\int[/tex]f(x)g(x)dx = F(x)g(x) - [tex]\int[/tex]F(x)g'(x)dx
    but I can't compute the integral of arctan(x).
    Could someone help me?
  2. jcsd
  3. Jan 14, 2009 #2


    Staff: Mentor

    Is this the integral?
    [tex]\frac{1}{\pi}\int_{-b}^b{\frac{x}{x^2 + 1}dx[/tex]

    If so, you can use a simple substitution, u = x^2 + 1, and du = 2xdx
  4. Jan 14, 2009 #3


    Staff: Mentor

    BTW, you should have posted this in the Calculus & Beyond forum. This problem clearly falls in that area.
  5. Jan 14, 2009 #4
    Seems kind of weird to be doing that integral from -b to b, whether or not b > 0 or < 0 you get into complex numbers.
  6. Jan 14, 2009 #5

    Gib Z

    User Avatar
    Homework Helper

    Perhaps the easiest way is to observe this function is odd, and look at the interval of integration.
  7. Jan 14, 2009 #6


    User Avatar
    Science Advisor

    No, you don't. You are squaring not taking square roots. As Mark44 said, use the substitution u= x2+ 1. Or, even simpler, use Gib Z's suggestion. This is really a very simple integral.
  8. Jan 14, 2009 #7
    Oh duh, good point.
  9. Jan 14, 2009 #8
    Yeah, sorry, I got it myself pretty soon after posting this. It feels like the more I study maths, the more I forget..!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook