Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}xds,$ where $C$ is

a$.$ the straight line segment $x=t,y=\frac{t}{2},$ from $(0,0)$ to $(12,6)$

b$.$ the parabolic curve $x=t,y=2t^2,$ from $(0,0)$ to $(3,18)$

a$.$ For the straight line segment, ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}xds=72\sqrt[\phantom{2}]{\frac{5}{4}}.($Type an exact answer.$)$

b$.$ For the parabolic curve, ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}xds=\frac{1}{48}({144}^{\frac{3}{2}}+1).($Type an exact answer.$)$