I.10.26 Flux of the vector field

condition: Find the flow of the vector field \( \vec{a}=x^{2} \vec{\imath}+x \vec{\jmath}+x z \vec{k} \) through part of the external side of the paraboloid of revolution \( \beta y=\alpha x^{2}+\gamma z^{2} \), located in the first octant and bounded by the plane \( y=\varepsilon \) \( (0 \leq y \leq \varepsilon) \) \[ \alpha=2, \quad \beta=4, \quad \gamma=2, \quad \varepsilon=4,5 \]