Given:

vec$(vec(F))=(4x^3{y}^2-2x{y}^3)hat(i)+(2x^{4}y-3x^2{y}^2+4y^3)hat(j)$

$C$:vec$(r)(t)=(t+sin(t))hat(i)+(2t+cos(t))hat(j),0t1$

$(5$ points$)$ Show that vec$(F)$ is conservative.

$(12$ points$)$ Find a potential function $f.$

$(8$ points$)$ Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)$ using the Fundamental Theorem