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Does line integral integrate over the projection of a 3d curve onto the x-y plane or over the 3d curve itself as the base of the integration? Thanks

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  • $\begingroup$ I know that there is a surface that makes, in relation to the line, a curtain and we integrate the area of this curtain. The surface is the height But I'm not sure about the base. It is always at z=0 even if the curve is 3d and moves in all directions? $\endgroup$ Commented 13 hours ago

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If we are integrating over a $3D$ curve, we can say 'base' of the integral is that curve itself, not the projection. Indeed, there is nothing special about $xy$-plane at all.

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