Let $M$ be the manifold with boundary $ M=\mathbb{R}_{\geq0}$ and $\omega\in\Omega^0(M)$ a 0-form.
Suppose both $\int_M d\omega$ and $\int_{\partial M}\omega$ are finite.
Does Stokes theorem hold? Or does $\int_M d\omega=\int_{\partial M}\omega$ hold?
I have no idea how to prove of disprove this and would appreciate any hints to get me in the right direction. Also I use this version of Stokes:
Stokes' Theorem: Let $M$ be a smooth, oriented $n$-manifold with boundary, and let $\omega$ be a compactly supported smooth $(n-1)$-form on $M$. Then $$\int_M d\omega = \int_{\partial M} \omega.$$