A simplified multidimensional integral

TL;DR

This paper introduces a simplified multidimensional integral that, while less general than the Riemann integral, is easier to compute and still applicable to most practical functions, with clear theorems and characterizations.

Contribution

It proposes a new simplified integral for functions of multiple variables, streamlining integral theorems and characterizations compared to traditional approaches.

Findings

Most practical functions are integrable under the new integral

Basic integral theorems are derived more quickly

Provides a characterization of integrable functions and primitives

Abstract

We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.