i.12.4 Vector field circulation

Calculate the circulation of the vector field \( \bar{a} \) through the closed loop \( L \) directly and using the Stokes formula: \[ \begin{array}{l} \vec{a}=(z x+y) \vec{\imath}+(z y-x) \vec{\jmath}-\left(x^{2}+y^{2}\right) \vec{k} \\ L:\left\{\begin{array}{l} x^{2}+y^{2}=1 \\ z=3 \end{array}\right. \end{array}\]