# The force applied on a moving object with a mass of 1 kg  on a linear path is given by F(x)=x^2+3. How much work would it take to move the object over x in [1,2] ?

Aug 27, 2017

$W = 5.33$ $\text{J}$

#### Explanation:

The equation for the work done by a varying force is given by

$W = {\int}_{{x}_{1}}^{{x}_{2}} {F}_{x} \textcolor{w h i t e}{l} \mathrm{dx}$

We know

• ${F}_{x} = {x}^{2} + 3$

• ${x}_{1} = 1$ $\text{m}$

• ${x}_{2} = 2$ $\text{m}$

Plugging these in:

color(red)(W) = int_(1color(white)(l)"m")^(2color(white)(l)"m") x^2 + 3color(white)(l)dx = color(red)(ulbar(|stackrel(" ")(" "5.33color(white)(l)"J"" ")|)