I'm evaluating a line integral written in the form:
$\int_{\partial\Omega_1} v\nabla u\cdot n$ where $\partial \Omega_1$ is simple curve forming one part of the boundary $\partial\Omega$ of a closed region, and $n$ is the unit normal to $\partial\Omega_1$.
Suppose C(t) is a positively oriented parameterization of $\Omega_1$. Since there is no differential explicitly indicated in the integral, can i automatically assume that the differential is $||C'(t)||dt$?