$12,13,14,15,16,17$ and $18$

$($a$)$ Find a function $f$ such that $F=$gradf and

$($b$)$ use part $($a$)$ to evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$ along the given curve $C.$

$13.F(x,y)=x^2{y}^{3}i+x^3{y}^{2}j,$

$C$:$r(t)=($:$t^3-2t,t^3+2t$:$),0t1$