Let $n,k\in\mathbb{N}$ with $1\le k\le n$, let $(S,\varepsilon)$ be an \reftext{def:oriented-k-sub-rectangle-euclidean-2026a}{oriented $k$-sub-rectangle} of $\mathbb{R}^n$, let $U\subseteq \mathbb{R}^n$ be open with $S\subseteq U$, and let $\omega$ be a \reftext{def:c1-differential-k-form-euclidean-open-set-2026b}{$C^1$ differential $(k-1)$-form} on $U$. Then

where $d\omega$ is the exterior derivative from \ref{def:exterior-derivative-c1-differential-form-euclidean-open-set-2026b}, the left-hand side and each term on the right are integrals in the sense of \ref{def:integral-form-oriented-k-sub-rectangle-euclidean-2026b}, and the boundary collection is the one from \ref{def:boundary-oriented-k-sub-rectangle-euclidean-2026a}.