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## Homework Statement

Consider a classical particle moving in a one-dimensional potential well u(x). The particle is in thermal equilibrium with a reservoir at temperature T, so the probabilities of its various states are determined by Boltzmann statistics. Show that the average position of the particle is given by [tex]\overline{x}=\frac{\int xe^{-(\beta)u(x)}\,dx}{\int e^{-(\beta)u(x)}\,dx}[/tex]

## Homework Equations

Partition function, equipartition theorem

## The Attempt at a Solution

I don't know where they get the integrals from, the partition function is a sum.

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