# The force applied on a moving object with a mass of 7 kg  on a linear path is given by F(x)=x . How much work would it take to move the object over x in [1,3] ?

Mar 6, 2018

$W = 4$ J

#### Explanation:

The force function:

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

Total work is force integrated through a distance:

${\int}_{1}^{3} F \left(x\right) \mathrm{dx}$

$= {\int}_{1}^{3} x \mathrm{dx}$

$= \frac{1}{2} {\left[{x}^{2}\right]}_{1}^{3}$

$= \frac{1}{2} \left(9 - 1\right) = 4$ J

Hence, $W = 4$ J.