# Difficulty following example in Taylor's Classical Mechanics

1. Sep 7, 2014

### cwbullivant

http://i.imgur.com/GP6QorG.jpg

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.

Last edited: Sep 7, 2014
2. Sep 8, 2014

### Delta²

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.