Calculate integral curvilinear using the theorem Stokes

$\displaystyle $\int\limits_\alpha {\left( {y - z} \right)dx + \left( {z - x} \right)dy + \left( {x - y} \right)dz}$$

Being $\displaystyle $\alpha $$ a customization of the curve given by the equations

$\displaystyle $\alpha$$ :

$\displaystyle $x^2 + 4y^2 = 1 \wedge x^2 + y^2 = z$$