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

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    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?

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

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    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 [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.
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