Use Stokes' Theorem to evaluate$\displaystyle \iint_M (\nabla \times \mathbf{F}) \cdot d\mathbf{S}$ where $M$ is the hemisphere $x^2 + y^2 + z^2 = 4, x \ge 0$, with the normal in the direction of the positive x direction, and $\mathbf{F} = \langle x^3, 0, y^2 \rangle$.
Begin by writing down the "standard" parametrization of $\partial M$ as a function of the angle $\theta$ (denoted by "t" in your answer)
$x =$, $y=$, $z=$.
$\int_{\partial M} \mathbf{F}\cdot d\mathbf{s} = \int_0^{2\pi}f(\theta)\,d\theta$, where
$f(\theta) =$ (use "t" for theta).
The value of the integral is .