# The force applied against a moving object travelling on a linear path is given by F(x)= x^2+4x. How much work would it take to move the object over x in [0,2] ?

Apr 9, 2018

The work is $= \frac{32}{3} J$

#### Explanation:

The work done

$\Delta W = F \Delta x$

THe force is $F \left(x\right) = {x}^{2} + 4 x$

$W = {\int}_{0}^{2} \left({x}^{2} + 4 x\right) \mathrm{dx}$

$= {\left[\frac{1}{3} {x}^{3} + 2 {x}^{2}\right]}_{0}^{2}$

$= \left(\frac{8}{3} + 8\right) - \left(0 + 0\right)$

$= \frac{32}{3} J$