  In this paper we define the notion of slow divergence integral along sliding
segments in regularized planar piecewise smooth systems. The boundary of such
segments may contain diverse tangency points. We show that the slow divergence
integral is invariant under smooth equivalences. This is a natural
generalization of the notion of slow divergence integral along normally
hyperbolic portions of curve of singularities in smooth planar slow-fast
systems. We give an interesting application of the integral in a model with
visible-invisible two-fold of type $VI_3$. It is related to a connection
between so-called Minkowski dimension of bounded and monotone "entry-exit"
sequences and the number of sliding limit cycles produced by so-called canard
cycles.
