Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2006 / Paper 2 / 4 / b

Choose $f=x^2(1+y)+y^{2}z-1$. Since $f_z=y^2>0$ on the stated open domain, its upward vector area element isThe graph becomes unbounded near parts of $y=0$; the flux integrals below are understood as limits from $y>0$.