# The force applied against a moving object travelling on a linear path is given by F(x)= x + 4. How much work would it take to move the object over x in [ 4 , 7] ?

Mar 22, 2018

The work is $= 28.5 J$

#### Explanation:

The force is

$F \left(x\right) = x + 4$

The work is

$\mathrm{dW} = F \mathrm{dx}$

Therefore,

$W = \int F \mathrm{dx}$

$= {\int}_{4}^{7} \left(x + 4\right) \mathrm{dx}$

$= {\left[\frac{1}{2} {x}^{2} + 4 x\right]}_{4}^{7}$

$= \left(\frac{49}{2} + 28\right) - \left(8 + 16\right)$

$= \frac{49}{2} + 4$

$= 28.5 J$