Compute the line integrals over plane curves, that is$,{\displaystyle \underset{C}{\overset{\phantom{}}{}}}(x,y)ds,$ where

$($a$)(x,y)=\frac{\sqrt[\phantom{2}]{y}}{x}$ and $C$ is the curve vec$(r)(t)=t^3$widehat$(i)+t^4$widehat$(j),1t2.$

$($b$)(x,y)=x+\sqrt[\phantom{2}]{y},$ and $C$ is the closed curve joining the curves $y=x^2$ from $(0,0)$ to $(1,1)$ and $y=x$ from $(1,1)$ to $(0,0).$

$($c$)(x,y)=x+y,$ and $C$ is the closed curve $x^2+y^2=4$ in the first quadrant from $(2,0)$ to $(0,2).$