# Path Integral to determine Work Done

## Main Question or Discussion Point

When doing a path integral to determine the work done by a particle :

http://latex.codecogs.com/gif.latex?\int&space;\textbf{w}\cdot&space;d\mathbf{s}

Where F is some vector. Now, I can't remember what ds is. I vaguely seem to remember that it is some unit vector parallel to and in the direction of the path of movement of the particle.

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## Answers and Replies

HallsofIvy
"ds" is what I would call "the vector differential of arc length". Specifically, if the path is given by the parametric equations, x= x(t), y= y(t), z= z(t), then $d\vec{s}= (dx/dt)\vec{i}+ (dy/dt)\vec{j}+ (dz/dt)\vec{j}$.