# Gaseous system: Meaning of this integral eq.

by jam_27
Tags: gaseous, integral, meaning
 P: 43 What is the physical or statistical meaning of the following integral $$\int^{a}_{o} g(\vartheta) d(\vartheta)$$ = $$\int^{\infty}_{a} g(\vartheta) d(\vartheta)$$ where $$g(\vartheta)$$ is a Gaussian in $$\vartheta$$ describing the transition frequency fluctuation in a gaseous system (assume two-level and inhomogeneous) . $$\vartheta = \omega_{0} -\omega$$, where $$\omega_{0}$$ is the peak frequency and $$\omega$$ the running frequency. I understand that the integral finds a point $$\vartheta = a$$ for which the area under the curve (the Gaussian) between 0 to a and a to $$\infty$$ are equal. But is there a statistical meaning to this integral? Does it find something like the most-probable value $$\vartheta = a$$? But the most probable value should be $$\vartheta = 0$$ in my understanding! So what does the point $$\vartheta = a$$ tell us? I will be grateful if somebody can explain this and/or direct me to a reference. Cheers Jamy