The vector field vec$(F)(x,y)=($:$5x+2y,2x+6y$:$)is$:

not conservative

$(If$ you answered "not conservative," enter DNE for the second part.$)$

A function $f(x,y)$ that satisfies vec$(F)(x,y)=$gradf$(x,y)is$:

$f(x,y)=$

$IfCis$ the curve parameterized $by$ vec$(r)(t)=($:$t^2,t^3$:$)$ for $0t3$ then:

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