5. As \(\vec{B} = \nabla \times \vec{A}\) then \(\phi_M = \iint \vec{B} \cdot d\vec{S} = \iint \nabla \times \vec{A} \cdot d\vec{S} = \oint \vec{A} \cdot d\vec{l}\) where the last equality
follows by Stoke's theorem. If \(\vec{A} = \hat{x}3x^2y^2 - \hat{y}x^3y^2\) calculate the magnetic flux through the
area bound by the rectangle (0, 0), (0, 2), (1, 2), (1, 0).