Find the line integral with respect to arc length $\displaystyle \int_C (3 x + 8 y) ds$, where $C$ is the line segment in the $xy$-plane with endpoints $P = \left(3,0\right)$ and $Q = \left(0,6\right)$.

(a) Find a vector parametric equation $\vec{r}(t)$ for the line segment $C$ so that points $P$ and $Q$ correspond to $t = 0$ and $t = 1$, respectively.
$\vec{r}(t) =$

(b) Using the parametrization in part (a), the line integral with respect to arc length is
$\displaystyle \int_C (3 x + 8 y) ds = \int_a^b$ $dt$
with limits of integration $a =$ and $b =$

(c) Evaluate the line integral with respect to arc length in part (b).
$\displaystyle \int_C (3 x + 8 y) ds =$