(Solved): 34 please 33-35. Flux integrals Compute the outward flux of the following vector fields across the ...

34 please

33-35. Flux integrals Compute the outward flux of the following vector fields across the given surfaces \( S \). You should decide which integral of the Divergence Theorem to use. 33. \( \mathbf{F}=\left\langle x^{2} e^{y} \cos z,-4 x e^{y} \cos z, 2 x e^{y} \sin z\right\rangle ; S \) is the boundary of the ellipsoid \( x^{2} / 4+y^{2}+z^{2}=1 \). 34. \( \mathbf{F}=\langle-y z, x z, 1\rangle ; S \) is the boundary of the ellipsoid \( x^{2} / 4+y^{2} / 4+z^{2}=1 \). 35. \( \mathbf{F}=\langle x \sin y,-\cos y, z \sin y\rangle ; S \) is the boundary of the region bounded by the planes \( x=1, y=0, y=\pi / 2, z=0 \), and \( z=x \)