I.10.28 Flux of the Vector Field

Condition: Find the flow of vector field \ (\ vec {a} = \ alpha \ vec {\ iMath}+\ beta \ vec {\ jmath}+\ gamma \ vec {k} \ quad \) through the surface of the cylinder \ ( x^{2}+y^{2} = r^{2} \), limited by the planes \ (z = 0, z = b \). \ [\ alpha = z-x, \ quad \ beta = y^{2} -z^{2}, \ quad \ gamma = x-z {,} \] \ [r = 3, \ quad b = 2 \]