i.12.7 Vector field circulation

Calculate the circulation of the vector field \( \bar{a} \) through the closed contour Г directly and using the Stokes formula: \[ \begin{array}{l} \vec{a}=(x-y) \vec{\imath}+(2 x+y) \vec{\jmath}+\left(x^{2}+2 z+4\right) \vec{k} \\ \Gamma: x^{2}+y^{2}=z-2, \quad z=0 \end{array} \]