Find the work done by the force field ( {F}(x,y)=langle -2x²,3yeˣ rangle ) on a particle that moves once along the parabola ( x=y²+5 ) from ( (5,0) ) to ( (14,3) ). The curve can be parametrized by expressing it as:
a) ( {r}(t) = langle t, √{t-5} rangle ), ( 5 ≤ t ≤ 14 )
b) ( {r}(t) = langle t²+5, t rangle ), ( 0 ≤ t ≤ 1 ) c) ( {r}(t) = langle t, t²+5 rangle ), ( 0 ≤ t ≤ 1 )
d) ( {r}(t) = langle t, 3t rangle ), ( {5}/{3} ≤ t ≤ {14}/{3} )