The Change of Variable Formula Integrals, do they have equal value?
Classical Analysis and ODEs
2025-06-24 v5
Abstract
Assuming that the two integrals in the Change of Variable Formula for the Riemann integral on the real line are finite, one can rightfully ask if they have equal value. We give a positive answer to this question. The proof is very easy to follow and to keep in mind. The result is extended to improper Riemann integrals. Three examples are given.
Keywords
Cite
@article{arxiv.2502.12679,
title = {The Change of Variable Formula Integrals, do they have equal value?},
author = {Oswaldo Rio Branco de Oliveira},
journal= {arXiv preprint arXiv:2502.12679},
year = {2025}
}
Comments
21 pages (three more than the previous version), 3 figures, two lemmas have been added, a corollary to Theorem 2 has been added, a remark about substitution maps has been added, a remark about Pompeiu derivatives has been added