I.10.5 Flux of the Vector Field

Calculate the field of the field \ (\ vec {a} \) through the surface \ (\ mathrm {s} \) using the Gauss-Ostrograd formula. \ [\ vec {a} = x y \ vec {\ iMath}+y \ vec {\ jmath} +2 z \ vec {k}, \ quad \ mathrm {~ s}: \ left \ {array} {l} {l} {l} {l} {l} {l} z = x^{2}+y^{2} \\ z = 4, \ quad (z \ geq 4) \ end {array} \ right. \]