Work done by non conservative force

hhhmmm...I don't remember my physiscs that well and what the difference between conservative and non-conservative force is...

...but are you sure you have a resulting work at the end? I mean, it may seem like there is area under the curve, but don't forget that your distance travel on the way back is of opposite sign as when going forward, and so, if you integrate that "area under the curve" is going to cancel out ...

does this make sense?

 

I think you have a misunderstanding. The work would be the area in the coordinate plane Force vs displacement. But, this is true only in a one-dimensional case. In more than one dimension, the force is a curvilinear integral:
[tex]
W = \int_{C}{\mathbf{F} \cdot d\mathbf{x}} = \int_{C}{F_{x} \, dx + F_{y} \, dy + F_{z} \, dz}
[/tex]
The force is non-conservative if the work is different for different contours in three-dimensional space between the same two points. There is no area that you can construct in this case.