Let S S be the upper hemisphere x 2 + y 2 + z 2 = 1 , z 0 x 2 + y

Let $S$ be the upper hemisphere $x^2+y^2+z^2=1,z\ge 0$. For each of the functions (a)-(d), determine whether \(\iint_{\mathcal{S}} f d S\) is positive, zero, or negative (without evaluating the integral). Explain your reasoning.
(a) \(f(x, y, z)=y^{3}\)
(b) \(f(x, y, z)=z^{3}\)
(c) \(f(x, y, z)=x y z\)
(d) \(f(x, y, z)=z^{2}-2\)