My question may be expressed with an example I'm most familiar with..
In many ocean science text books, the mean density of the water column is expressed as $${\widehat\rho}=\int^0_{-h}\rho(z)dz$$
How can this be the mean? Surely you need $1/(b-a)$ (i.e. $1/(-h - 0)$) at the beginning of the RHS of the equation? Why don't the text books show it?
Kind regards,
Mark