Physics - W.E.P. Question with Solution | TestHub

The work done by a variable force $F(x)$ from $x_1$ to $x_2$ is given by $W={\int }_{x_1}^{x_2}F(x)dx$. Here, $F(x)=2x^2-3x+5$, $x_1=0$, and $x_2=4$. So, $W={\int }_0^4(2x^2-3x+5)dx={\left[\frac{2x^3}{3}-\frac{3x^2}{2}+5x\right]}_0^4$. Evaluating this, $W=\left(\frac{2(4{)}^3}{3}-\frac{3(4{)}^2}{2}+5(4)\right)-0=\left(\frac{128}{3}-\frac{48}{2}+20\right)=\left(42.67-24+20\right)=38.67\text{ J}$.