I.10.23 Flux of the vector field

Condition: Find the flow of the vector \( \vec{a}=2 x \vec{\imath}-(x+y) \vec{\jmath}+z^{2} \vec{k} \) through: a) the full surface of the cylinder \[ x^{2}+z^{2}=4, y=0, y=2 \] b) the base of this cylinder, lying in the plane \( y=2 \), in the positive direction of the axis \( O Y \).