I.10.35 Flux of the Vector Field

Condition: Find the flow of vector field \ (\ vec {a} \) through a closed surface \ (s \) (normal external) using the formula of Ostrogradsky-guuss. Having chosen the side of the surface, find the vector field directly \ (\ vec {a} \) through the surface \ (s_ {1} \), which is part of the surface \ (s \) and determined by the specified equations. \ [\ vec {a} = 2 x^{2} y \ vec {\ iMath}+x y^{2} \ vec {\ jmath}+(z-2) \ vec {k} \] \ ( S: \ left \ {\ begin {array} {c} z = 2-x^{2} -y^{2} \\ z \ geq 0 {array}, \ quad S_ {1}: z = 2-x^{2} -y^{2} \ right.