A force F → = 2 + 3 x i ^ acts on a particle in the x direction where F is in Newton and x is in meter…

The formula to calculate the work done by a variable force is given by

$W={\int }_{x_1}^{x_2}Fdx ...\left(1\right)$

Substitute the values of the known parameters into equation (1) to calculate the required work done.

$\begin{array}{rcl}W& =& {\int }_0^4 (2+3x)dx\\ & =& {\left[2x+\frac{3}{2}{x}^2\right]}_0^4\\ & =& [8+24] \mathrm{J}\\ & =& 32 \mathrm{J}\end{array}$