The vector field vec$(F)=($:$x^3{y}^4,x^4{y}^3$:$)is$:

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

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

$f(x,y)=$

$IfCis$ the curve parameterized $by$ vec$(r)(t)=($:$5cos(t),5sin(t)$:$)$ for $0t\frac{}{4}$ then:

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