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For some reason, I'm having a mental block on how to answer this one:

Consider the force function:

F = ix + jy

Verify that it is conservative by showing that the integral,

[tex] \int F \cdot dr [/tex]

is independent of the path of integration by taking 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).

Now I've already verified that it is conserved by taking the curl of F, but I can't seem to come to a similiar conclusion using the path integrals. Can someone help me out with this one? At the very least, if I could see the integrals themselves for each path, perhaps I could figure out where I've made my mistake. Thanks.