### Still have math questions?

If $$F = x ^ { 2 } z i + ( y ^ { 2 } z + 3 y ) j + x ^ { 2 } k ,$$ find the flux of $$F$$ across the part of the ellipsoid $$x ^ { 2 } + y ^ { 2 } + 4 z ^ { 2 } = 16 ,$$ where $$z \geq 0$$ oriented with upward normal.
$$128 \pi$$