Let vec$(F)(x,y)=($:$x{y}^2,x^{2}y$:$)$

a$)$ Determine whether vec$(F)$ is conservative

b$)$ If vec$(F)$ is conseconative, first the percentai froction on use it along with the fundamant Theorem for Line integral to evaluate ${\displaystyle \underset{c}{\overset{\phantom{}}{}}}$vec$(F)*kvec(r),$ where $c$ is the creve given b$)$

vec$(r)(t)=($:$tsin(\frac{}{2}t),tcos(\frac{}{2}t)$:$),0t1,If$