I.10.2 Flux of the Vector Field

Condition: Find the flow of the vector field \ (\ vec {f} \) through the closed surface \ ((\ omega) \): \ [\ begin {array} {l} \ vec {f} = 3 x^{2} \ \ imath} +2 x^{2} y | \ vec {\ jmath}+(2 x-1) z \ vec {k} \\ \ omega: x^{2}+y^{2} \ leq 1, \ quad z \ geq 0, \ quad Z \ leq 1 \ End {Array} \] \]