When a force F → = 17 - 2 x + 6 x 2   N acts on a body of mass 2   kg and displaces it from…

Work done on a body by a force is the product of force and the displacement of the body due to force in the same direction, or work is the dot product of the force and the displacement vectors.

$$\begin{gathered} W=\overrightarrow{F}·\overrightarrow{s} \\ \Rightarrow \int dw={\int }_{x_i}^{x_f}F.dx \\ \Rightarrow \int dw={\int }_{x_i=0 \mathrm{m}}^{x_f=8 \mathrm{m}}\left(17-2x+6x^2\right)dx \\ \Rightarrow W={\left[17x-\frac{2x^2}{2}+\frac{6x^3}{3}\right]}_{x_i=0 \mathrm{m}}^{x_f=8 \mathrm{m}} \\ \Rightarrow W=1096 \mathrm{J} \end{gathered}$$