Compute the flux \(\oint_{\partial \mathcal{D}} \mathbf{F} \cdot \mathbf{n} d s\) of \(\mathbf{F}(x, y)=\left\langle x^{3}, y x^{2}ightangle\) across the unit square \(\mathcal{D}\) using the vector form of Green's Theorem.

THEOREM 1 Green's Theorem Let D be a domain whose boundary 3D is a simple closed curve, oriented counterclockwise. If F and F2 have continuous partial deriva- tives in an open region containing D, then a F FOD F dx + F dy = [[ ( x a F y d'A