A position dependent force $F=7-2x+3x^2$ newton (where x is in meter) on a small body of mass 2 Kg & displace it from $x=0$  to $x=5$ m. Calculate the work done.

$\text{Step 1: Work done}$

Work done for small displacement  can be defined as:

 $dW=Fdx$           $....(1)$

$\text{Step 2: Integrate the equation}$

Total work done can be calculated by integrating the equation $(1)$ with limits $x=0$ to $x=5m$ 

  $\int dW=\underset{0}{\overset{5}{\int }}Fdx$

 $\int dW=\underset{0}{\overset{5}{\int }}\left(7-2x+3x^2\right)dx$

 $\Rightarrow W={\left[7x-\frac{2x^2}{2}+\frac{3x^3}{3}\right]}_0^5$

 $\Rightarrow W=35-25+125=135J$

Hence, the work done is $135J$