Results 1 to 2 of 2

Math Help - Complex Integral

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    6

    Complex Integral

    Show that

    \frac{1}{2 \pi} \int_{-\pi}^{\pi} \frac{1}{1-2r\cos \theta +r^2} d \theta = 1, 0 \leq r < 1.

    Right now, I don't see how to show this. I do see that the integrand is an even function if that helps at all. Also, since this is not from -\infty to \infty, I do not know the method to proceed. I need a few hints on how to start.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2008
    Posts
    903
    Hi. If I use the z=e^{it} substitution, then I get:

    \int_{-\pi}^{\pi}\frac{1}{1-2 r\cos(t)+r^2}dt=-i\oint \frac{dz}{(r-z)(rz-1)}=\frac{2\pi}{1-r^2},\quad |r|<1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Complex Integral in Complex Analysis
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: August 21st 2011, 10:46 PM
  2. Complex Integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 3rd 2010, 05:30 PM
  3. Complex integral help
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 9th 2009, 07:08 AM
  4. complex integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 25th 2009, 07:44 PM
  5. Complex integral help
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: March 20th 2009, 10:48 AM

Search Tags


/mathhelpforum @mathhelpforum