Let $\vec { F } = x z \vec { i } + y z \vec { j } + 9 x ^ { 2 } y ^ { 2 } \vec { k }$

Essay

Let $\vec { F } = x z \vec { i } + y z \vec { j } + 9 x ^ { 2 } y ^ { 2 } \vec { k }$ .Calculate the flux of $\vec { F }$ through the surface oriented upward and given by z = f(x, y)= xy, over the region in the xy-plane bounded by the curves $y = x ^ { 2 }$ and $y = x ^ { 3 }$ between the origin and the point (1, 1).