PHY2061 R. D. Field Department of Physics line_1.doc Univesity of Florida P1Closed LoopLine Integral of a Vector Function Let zzyxFyzyxFxzyxFzyxFzyxˆ),,(ˆ)..(ˆ),,(),,(++=!be a vector function of position. In general, the line integral of ),,(zyxF!depends of the start point P1, and the end point P2and the path chosen from P1to P2(curve C): ∫⋅=CurveCrdFPathPPI!!),,(21, where I(P1,P2,Path) is the component of along the path integrated over the path, ∫∫∫++==⋅CurveCCurveCzyxCurveCdzFdyFdxFdrFrdF)(cosθ!!. Remark: If 0=×∇F!!then I(P1,P2,Path) = I(P1,P2) and is only a function
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