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 {k} \) through the outer side of the rotation paraboloid \ (\ beta y = \ alpha x^{2}+\ gamma z^{2} \), located in the first octant and a limited plane \ (y = \ varepsilon \) \ ((0 \ leq y \ leq \ varepsilon) \) \ [\ alpha = 2, \ quad \ Beta = 4, \ Quad \ Gamma = 2, \ Quad \ Varepsilon = 4.5 \]