Before revision:  This results due to the possible decomposition of an arbitrary n-volume into an integral of statistically weighted volumes of n-spheres  .
After revision:  This results due to the possible decomposition of an arbitrary n-volume into an integral of statistically weighted volumes of n-spheres . We establish its dimensional scaling, and extend it for evaluation of arbitrary integrals over non-convex domains. Our results also show that this method is significantly more efficient than the MCMC approach even when restricted to convex domains, for n \sim < 100. An importance sampling may extend this advantage to larger dimensions .