9.8.3 Surface integrals

(3) Problem: Calculate the integral using Stokes formula. \[ \int_{\Gamma} x y z d x+y^{2} z d y+z x^{2} d z \] where \( \Gamma \) is the curve: \( \left\{\begin{array}{l}x^{2}+z^{2}=a^{2}, a>0 \\ y^{2}+z^{2}=a^{2}, x \geq 0\end{array}\right. \) is positively oriented on the outer side of the first cylinder.