Answer
$\dfrac{7}{3}$
Work Step by Step
Work done$W=\int_C F\cdot dr=\int_0^{1} \lt2t-t^2,-t^2 +3t-1, 1-t-4t^2 \gt \cdot \lt 2,1,-1 \gt dt$
$=\int_0^{1} 2(2t-t^2)+(-t^2 +3t-1)-( 1-t-4t^2) dt$
$=\int_0^{1} 4t-2t^2-t^2 +3t-1- 1+t+4t^2 dt$
$=\int_0^{1} t^2+8t-2dt$
$=[\dfrac{t^3}{3}+4t^2-2t]_0^1$
$=[\dfrac{1^3}{3}+4(1^2-0)-2(1-0)]_0^1$
$=\dfrac{1}{3}+4-2$
$=\dfrac{7}{3}$
