Efficient α-Dense Curve Strategies for Multiple Integrals over Hyper-rectangle Regions

In this paper, we propose an approximation technique to compute multiple integrals of a non-negative real continuous function over a hyper-rectangle Ω of ℝⁿ. The main idea is to use a reducing transformation procedure obtained by using α-dense curves. First, the region Ω_f whose measure represents the value of the integral, is densified by a specific curve ℓ_α(t) of finite length. Therefore, the multiple integral can be approached by a simple integral corresponding to ℓ_α (t). Some numerical examples are given.