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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 $||C'(t)||dt$?

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    let us [continue this discussion in chat](http://chat.stacke$x$change.com/rooms/4821/discussion-between-michael-boratko-and-paul)2012-09-14

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