Approximating multiple integrals via α‐dense curves Available to Purchase

This paper is intended to provide a numerical method for computing integrals of several variables. The method is based on a intuitive geometric idea relative to the meaning of densifying a domain in Rⁿ⁺¹(n≥1) by a curve h(t), contained in that domain, say K, with a very small density α (this must be interpreted as the following property: for any point of K there exists a point of the curve at distance less or equal than α).Thus, the method states that any area, volume, etc, can be computed as the limit of the length of a certain curve, densifying that domain, multiplied by a power of its density. Therefore, the computation of a multiple integral of a nonnegative continuous function can be approached by a simple integral corresponding to the length of the curve h(t) and certain power of its density.