Suppose $\vec{F}(x,y) = (2 x + 3 y)\vec{i} + (3 x + 2 y)\vec{j}$. Evaluate the line integral for each of the given paths, which are comprised of line segments and arcs of circles.

(a) If $C$ is the open semicircular path in figure I of radius $3$ oriented counterclockwise, then
$\displaystyle \int_C \vec{F} \cdot d\vec{r}$ =

(b) If $C$ is the open piecewise linear path in figure II from $(3,0)$ to $(0,-3)$ to $(-3,0)$, then
$\displaystyle \int_C \vec{F} \cdot d\vec{r}$ =

(c) If $C$ is the closed path in figure III along the boundary of a semi-disk of radius $3$ oriented counterclockwise, then
$\displaystyle \int_C \vec{F} \cdot d\vec{r}$ =