Consider the vector field vec$(F)=($:$2x+7y,7x+3y$:$).$

Is this vector field Conservative?

Use method of your choice to evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)$ along the curve $C$:vec$(r)(t)=t^2$vec$(i)+t^3$vec$(j),$ for $0t2.$

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=$