I.10.4 Flux of the Vector Field

Calculate the field of the field \ (\ vec {a} \) through the closed surface S according to the formula of the Ostrogradsky Gouse. \ [\ vec {a} = x y \ vec {\ iMath}+y \ vec {\ jmath} +2 \ vec {k}, \ quad \ mathrm {~ s}: \ left {\ bein} {lr} {lr} {lr} {lr} {lr} x^{2}+y^{2}+z^{2} = 16 \\ z = 1, \ quad (z \ geq 1) \ end {array}. \ Right. \]