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

• March 15th 2012, 10:28 AM
DangerousDave
Vector calculus: Significance of V.(vectorial)dx in line integral
A quick query regarding the significance of integrating V.dx along some line (i.e. the dx is vectorial as well as the field V). Does this mean you dot product V with idx or something else?

Thanks
• March 16th 2012, 12:04 AM
Ridley
Re: Vector calculus: Significance of V.(vectorial)dx in line integral
• March 16th 2012, 05:33 AM
HallsofIvy
Re: Vector calculus: Significance of V.(vectorial)dx in line integral
If the problem really does say " $\int \vec{V}\cdot \vec{dx}$", then, yes, that is the integral in the x direction and so should be the unit vector $\vec{i}$.

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