$(a)$ Let $F(x,y)=(xy,y^2)$ and let $cbe$ the path $y=2x^2$

joining $(0,0)to(1,2)in{R}^2.$ Evaluate ${\displaystyle \underset{c}{\overset{\phantom{}}{}}}F*ds.$

$(b)$ Does the integral $in$ part $(a)$ depend $on$ the path

joining $(0,0)to(1,2)?$