I´m a little stuck with this problem, I think is false but I can´t find a counter example, here is the problem
Let $\omega$ a 1-form defined in $U\subset \mathbb{R^{2}}$(it can be $\mathbb{R^{n}}$, but I think is easy to think it at first in $\mathbb{R^{2}}$) and let $\gamma:[a,b]\rightarrow U$ a differentiable curve such that $\left | \omega _{\gamma(t)} \right |<k$ for all $t\in [0,1]$ Is it true that exists $\sigma=constant$ such that $\left | \int _{\gamma}\omega\right |\leq k\sigma$?
thanks for any help!