A force $F(x)=(-4\mathrm{.}0x^2+8\mathrm{.}0x)Nhat(i)$ acts on a particle as it moves along the $x-$axis.

Part $($a$)$

How much work, in joules, does the force do on the particle as it moves from $x=2\mathrm{.}02m$ to $x=5\mathrm{.}11m?$

$W=$

$$ J

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Part $($b$)$

If this force is a conservative force, what is the change in the potential energy, in joules, of the particle?