A box integral for dimension n with parameters q and s is defined as the expectation of distance from a fixed point q of a point r chosen at random over the unit n-cube, X_n(s, q) = integral_0^1 ... integral_0^1_︸_n [(r_1 - q_1)^2 + ... + (r_n - q_n)^2]^(s/2) d r_1 ...d r_n .

hypercube line picking | hypercube point picking | unit cube | unit square | unit square integral