Exercise:

If vec$(F)=x^2$hat$()+$xyhat$(),$ evaluate ${\displaystyle \underset{C}{\overset{{\displaystyle \underset{L}{\overset{\phantom{}}{}}}\text{v}\text{e}\text{c}(F)}{}}}$vec$(F).$ dvec$(r)$ from $(0,0)$ to $(1,1)$

$($a$)$ along the line $y=x$

$($b$)$ along the parabola $y=\sqrt[\phantom{2}]{x}$