# Multiple integral over a function of a vector

1. Oct 18, 2011

### wasia

Hello!

I want to calculate an integral of the form

$$\int d \vec k f(\vec k \cdot \vec x) g(k^2) \vec k,$$

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.

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