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Multiple integral over a function of a vector

  1. Oct 18, 2011 #1
    Hello!

    I want to calculate an integral of the form

    [tex] \int d \vec k f(\vec k \cdot \vec x) g(k^2) \vec k, [/tex]

    where k and x are 3-dimensional vectors and integration spans the whole 3D volume. I wonder what is the
    general approach to the problem? Were it not for the vector k term in the integral, one could just switch to
    the spherical coordinates and perform integration over two variables (|k| and one of the angles, while the other
    angle gives just a constant factor). But now it is not clear how to do that, since the result of the integration
    is supposed to be a 3-vector itself.

    Any suggestions or references are welcome.
     
  2. jcsd
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