### Stokes and Gauss' Theorem

1. A vector ﬁeld v(x, y, z) is given by the formula v(x, y, z) = xyˆx − yˆ2y. Consider a square path in the xy plane which starts at (0,0,0) and moves along the corners (1,0,0), (1,1,0) and (0,1,0). Calculate the path integral of v, i.e. v · dr, and calculate the area integral of the divergence, R ∇ × v · da, an