i.12.6 Vector field circulation

Calculate directly and using the Stokes formula the circulation of the vector field \( \bar{a} \) through the closed loop \( L \), given parametrically: \[ \vec{a}=y \vec{\imath}+x^{2} \vec{\jmath}-z \vec{k}, \quad L:\left\{\begin{array}{c} x^{2}+y^{2}=16 \\ z=3 \end{array} .\right. \]