The author investigates the evaluation of an integral \(I = \int_V g(v)\,dv\), with \(g(v): V \to \mathbb R\) being a positive, bounded, and continuous function defined on a bounded, symmetric, multi-dimensional compact real interval. The standard Monte Carlo method is used for evaluation, with a distribution density function \(p(v)\) that is proportional to the normalized Strang-Fix approximation of the integrand \(g(v)\), \(p(v)\) being built on the uniform grid with the step \(h\) in the domain \(V\). The author considers the mean value of time required for modelling the sampling value of the random variable with respect to the density \(p(v)\), and the asymptotic behaviour of this mean value is analyzed for the grid step \(h \to 0\).