An Elementary but Logical Approach to Integration

TL;DR

This paper introduces a simplified yet rigorous approach to integration suitable for undergraduates, bridging basic calculus and advanced theories like Lebesgue integration.

Contribution

It proposes a new elementary method for integration that enhances understanding and serves as a foundation for more complex integration theories.

Findings

Provides an accessible alternative to Riemann integrals.

Facilitates transition from basic calculus to Lebesgue integration.

Enhances conceptual clarity in integration teaching.

Abstract

We present a replacement for traditional Riemann integrals in undergraduate calculus, which supplements naive precalculus and at the same time opens a way to more sophisticated theories such as Lebesgue integration.