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

Simple integral in Mathematica

  1. Aug 23, 2011 #1
    The integral is :

    [PLAIN]http://i038.radikal.ru/1108/ed/a6cd0c5e8f36.jpg [Broken]

    , where "y" - coordinate, "kx" - component of wave vector

    if we calculate this integral on a paper with a pen and using compex variables theory we obtain:

    1) y>0

    here, in the capacity of contour we take semicircumference in the upper half plane


    2) y<0

    here, in the capacity of contour we take semicircumference in the lower half plane


    So the total answer is


    Let's calculate it in Math now.


    I wonder where Math gets "-" in Exp[] ?
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Aug 23, 2011 #2


    Staff: Mentor

    The - sign is correct. You made an error doing it by hand. To check do a numeric integration and compare to the analytical answers.
  4. Aug 23, 2011 #3
    ok, but where is an error?
  5. Aug 24, 2011 #4
    Looks to me you got the y's mixed up. When the semicircle is over the upper half-plane, I obtain an integral asymptotic to:

    [tex]\int_{0}^{\pi} e^{R\sin(t) y} dt[/tex]

    and that converges when y<0. Similar dif for the lower half-plane.
  6. Aug 24, 2011 #5
    i'm sorry, but where is "-" in Exp[] ?
  7. Aug 24, 2011 #6
    Let [itex]q=Re^{it}[/itex] over the semi-circle in the upper half-plane, and I want to know the bounds on the integral. So, I can write that it's less than:


    and really, it's going to be dominated by the real part of the exponent in the numerator right? So asymptotically, I (think), it's going to approach:



    So now, I'm only interested in the absolute value of that and that's dependent on it's real part:


    But I did that really quick and sloppy. Would need to double-check it and do a better job with inequalities and all if I were turning it in for a grade.
  8. Aug 24, 2011 #7
    you are right, i'm sorry. thanks!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Simple integral Mathematica
MATLAB Double Numerical Integration
MATLAB Integrating Trisurf
Mathematica Complex output from a real integral
Maple Computing Numerical Integrals with Maple
LaTeX \vec command