$[-/1$ Points$]$

Consider the following.

C$.$ counterclockwise around the triangle with vertices $(0,0),(1,0),$ and $(0,1),$ starting at $(0,0)$

$($a$)$ Find a plecewise smooth parametriation of the path $C.$

$r(t)=\{\begin{array}{c}0t1\\ 1t2\\ 2t3\end{array}$

$($b$)$ Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}(x2\sqrt[\phantom{2}]{y})ds.$