Difficulty following example in Taylor's Classical Mechanics

AI Thread Summary
The discussion focuses on the confusion surrounding the integration process in Taylor's Classical Mechanics, specifically regarding the components of force F. Participants clarify that Fx and Fy represent the components of the force rather than its partial derivatives. It is emphasized that along the path from O to Q, only the x component contributes to work, while the y component does not since it is perpendicular. Conversely, along the path from Q to P, only the y component does work, as the x component remains constant. The key takeaway is the distinction between force components and their contributions to work along specified paths.
cwbullivant
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I don't follow the integration in it.

I'm assuming Fx(x,0) and Fy(1,y) are the partial derivatives of F with respect to x and y, respectively, but given that, I can't seem to get my head around the result where the partial with respect to x is Fx = (x, 0) instead of Fx = (0, 2), and similar for y.
 
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They are not the partial derivatives , they are the x and y component of the F force. In the straight path from O to Q its only the x component that does work (y component is always perpendicular). In the path from Q to P its only the y component that does work.

The x component in the path from O to Q is zero because the force is F=(y,2x) so the x component is simply y but y=0 along this path. Similarly the y component from Q to P is simply 2x, but x=1 always for this path so the y component is 2.
 

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