Confirm that the force field F is conservative in some open connected region containing the points P and Q, and then find the work done by the force field on a particle moving along an arbitrary smooth curve in the region from P to Q.

1. F (x, y) = xy ² i + x ² y j ; P(1, 1), Q (0,0)

2. F (x, y) = 2xy ³ i + 3x ² y ² j ; P(-3, 0), Q (4,1)