  Analytic relations are derived for finite volume integrals over the radial
distribution function of a fluid, so-called Kirkwood-Buff integrals. Closed
form expressions are obtained for cubes and cuboids, the system shapes commonly
employed in molecular simulations. When finite volume Kirkwood-Buff integrals
are expanded over inverse system size, the leading term depends on shape only
through the surface area to volume ratio. This conjecture is proved for
arbitrary shapes and a general expression for the leading term is derived. From
this, a new extrapolation to the infinite volume limit is proposed, which
converges much faster with system size than previous approximations and thus
significantly simplifies the numerical computations.
