Evaluate $\displaystyle \iint_M (\nabla \times \mathbf{F})\cdot d\mathbf{S}$, where $M$ is the surface $x^2 + y^2 + 4 z^2 = 1, z \le 0$ and $\mathbf{F} = y\mathbf{i} - x\mathbf{j} + zx^3y^2\mathbf{k}$.
$\displaystyle \nabla \times \mathbf{F} = ($ ,,$)$.
Write the surface $M$ as a function $z = f(x,y)$. Then
$\displaystyle \iint_M (\nabla \times \mathbf{F})\cdot d\mathbf{S} = \int_a^b\int_{g(x)}^{h(x)} V(x,y) dy\,dx$
$a =$ , $b =$
$g(x) =$ , $h(x) =$
$V(x,y) =$
The value of $\displaystyle \iint_M (\nabla \times \mathbf{F})\cdot d\mathbf{S} =$.