Determine whether each of the following line integrals is indepen- dent of path. If it is, find a function h such that dh = Pdx + Qdy. If it is not, find a closed path around which the integral is not zero. (a) xdx+ydy, (b) xdx+ydy, (c) y dx+xdy, (d) y dx - xdy. Solution We compute the partial derivatve because if h exist we have that dh = Pdx+Qdy where OP/ay=aQ/dx. (a) P = x = 0 Q = y = 0 (b) Pdx=+9(y) SQdy = + f (x) h = x+ y P = x Q = y5 0 0 ay Pdx=+9(y) Qdy = % + f (x) h= 2x+y