Solution
= Solution
{c}
Take counterclockwise traversal as viewed from $z>0$. In the plane $z=0$, the <work> is the planar <line integral> of $P=2x-y$ and $Q=x+y$. <Green's theorem> gives
$$
\boxed{W=\oint_C(P\,dx+Q\,dy)
=\iint_{x^2+y^2\leq9}(1-(-1))\,dx\,dy
=2\pi(3^2)=18\pi.}
$$
The $z$ component contributes nothing because $dz=0$. The question specifies one circuit without specifying its direction: clockwise traversal gives $\boxed{-18\pi}$.