Find the counterclockwise circulation and outward flux for the field \[ \F = 2xy\i - y\j \] over the unit square $0\le x,\,y\le 1.$
Find the counterclockwise circulation and outward flux of the field \[ \F = (x-y)\i + (2x+y)\j \]
over the region enclosed by $y=x^2,\,0\le x\le 1$ and $y=\sin(\frac\pi2x),\,0\le x\le1.$