Compute the flux \(\oint_{\partial \mathcal{D}} \mathbf{F} \cdot \mathbf{n} d s\) of \(\mathbf{F}(x, y)=\left\langle x^{3}+2 x, y^{3}+yightangle\) across the circle \(\mathcal{D}\) given by \(x^{2}+y^{2}=4\) 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 |$ Fidx + F2dy = SS (/ (357 aD a Fi dA