Consider the two force functions
(a) F = ix + jy
(b) F = iy − jx
Verify that (a) is conservative and that (b) is nonconservative by showing that the integral ∫F ∙ dr is independent of the path of integration for (a), but not for (b), by talking two paths in which the starting point is the origin (0, 0), and the endpoint is (1, 1). For one path take the line x = y. For the other path take the x-axis out to the point (1, 0) and then the line x = 1 up to the point (1,1).
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