# The force applied against an object moving horizontally on a linear path is described by F(x)= x^2 + x N . By how much does the object's kinetic energy change as the object moves from  x in [ 1 , 2 ]?

Jun 11, 2018

The change in kinetic energy is $= 3.83 J$

#### Explanation:

The change in kinetic energy is equal to the work done.

$\Delta K E = W = F \times d$

$W = {\int}_{1}^{2} \left({x}^{2} + x\right) \mathrm{dx}$

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

$= \left(\frac{8}{3} + 2\right) - \left(\frac{1}{3} + \frac{1}{2}\right)$

$= \frac{14}{3} - \frac{5}{6}$

$= \frac{23}{6} = 3.83 J$