i.10.8 Flux of the vector field

Calculate the vector field flux \( \vec{a}=y z \vec{\imath}+ \) \( z x \vec{\jmath}+x y \vec{k} \) through the lateral surface of the cylinder directly and using the Gauss-Ostrogradsky formula: \[ x^{2}+y^{2}=a^{2}, \quad z \geq 1, \quad z \leq h \]