1. (a) Set up a path integral, and compute the work done by the force F =( x^2 - y^2) i + 2xyj by moving a particle of mass m, along the square in the plane, bounded by the coordinate axes and lines x = 3, y = 3 with the counterclockwise orientation.
(b) Compute the path integral F · dS where F = (x^2 - y^2) i + xj and C is one circuit of the circle C (x^2) +(y^2)= 4 in the counterclockwise direction.