Lets say we want to find the flux of some vector field over some surface $ f(x,y)$.
$\int \int_{S}^{} \overrightarrow{F}(x,y)*\overrightarrow{dA} $
What we do is we write $\overrightarrow{dA} = \overrightarrow{n}*dxdy$ where $\overrightarrow{n}$
is the normal vector of the surface at its every point.
$\overrightarrow{n} = (-\frac{\partial f}{\partial x} , -\frac{\partial f}{\partial y},1)$
Then we performe dot product of the vector field $\overrightarrow{F}(x,y)$ with $ \overrightarrow{n} $ and in the end we end up with a double integral.
Now suppose we want to calculate the integral $\int_{C}^{}\overrightarrow{F}(x,y)*\overrightarrow{dl}$
is there a similar way to do this just like with the flux without need of parameterization of the curve $C$?