Question $6(10$ points$)$

Given $F(x,y)=($:$4x^3{y}^2-2x{y}^3,2x^{4}y-3x^2{y}^{2}4y^3$:$)$

i$.$ Show $F(x,y)$ is conservative and find a potential function.

ii$.$ Use the Fundamental Theorem of Line Integrals to evaluate

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$ where $C$ is the curve represented by

$r(t)=(e^{t}sin(t))i(2e^{t}cos(t))j,0t1$

$$