(Solved): Find the line integral with respect to arc length C(6x+7y)dsx where C is the line segment ...

Find the line integral with respect to arc length ${?}_C(6x+7y)d{s}_x$ where $C$ is the line segment in the $xy$-plane with endpoints $P=(4,0)$ and $Q=(0,6)$. (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 ${?}_C(6x+7y)ds={?}_a^{b}dt$ with limits of integration $a=$ and $b=$ (c) Evaluate the line integral with respect to arc length in part (b). ${?}_C(6x+7y)ds=$