Vector calculus: Significance of V.(vectorial)dx in line integral

A quick query regarding the significance of integrating** V**.d**x **along some line (i.e. the dx is vectorial as well as the field V). Does this mean you dot product **V** with **i**dx or something else?

Thanks

Re: Vector calculus: Significance of V.(vectorial)dx in line integral

Re: Vector calculus: Significance of V.(vectorial)dx in line integral

If the problem really does say "$\displaystyle \int \vec{V}\cdot \vec{dx}$", then, yes, that is the integral in the x direction and so should be the unit vector [itex]\vec{i}[/itex].

More common is [tex]\int \vec{V}\cdot d\vec{s}[/itex] which is the dot product of [itex]\vec{V}[/itex] with the differential along the direction of the curve- the differential times the unit tangent vector to the curve.