and
integration over supermanifolds, Berezin integral, fermionic path integral
Kontsevich integral, Selberg integral, elliptic Selberg integral
A Berezinian integral is an integral over a supermanifold that is a superpoint $\mathbb{R}^{0|q}$.
For the infinite-dimensional version see fermionic path integral.
An exposition of the standard lore is here:
A general abstract discussion in terms of D-module theory is in