# Integrating over the phase in Mathematica

1. May 16, 2012

### nickthequick

Hi,

I have a question about integrating over the phase of a function in Mathematica. The origins of this problem is in scale analysis.

$f(x,t)= \sum_n a_n \cos (n(kx-\omega t))$

for $k,\omega \in \mathbb{R}$. I want to integrate an expression dependent on f over the phase

$\theta_n = n(kx-\omega t)$ from $[0,2\pi]$. more specifically, I want to find

$\int_0^{2\pi} g(x,t) \ d \theta$ where, for instance, $g(x,t) = f_t + 1/2f_^2+ f^2$.

Is there any automated way to do this without having to go back and manually change the phase to be a single symbolic variable?

Thanks!

Nick

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