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

Is this vector field Conservative? $$ Conservative $$

If so:

Find a function $f$ so that vec$(F)=$gradf

$f(x,y)=K$

Use your answer to evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)$ along the curve $C$:vec$(r)(t)=5cos(t)vec(i)5sin(t)vec(j),0t\frac{}{4}$

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