# The force applied against an object moving horizontally on a linear path is described by F(x)=x^2-x+4. By how much does the object's kinetic energy change as the object moves from  x in [ 2, 4]?

##### 1 Answer
Jul 24, 2017

The change of kinetic energy is $= 20.7 J$

#### Explanation:

The change of kinetic energy is equal to the work.

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

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

$= {\left[{x}^{3} / 3 - {x}^{2} / 2 + 4 x\right]}_{2}^{4}$

$= \left(\frac{64}{3} - 8 + 16\right) - \left(\frac{8}{3} - 2 + 8\right)$

$= \frac{56}{3} + 2$

$= \frac{62}{3}$

$= 20.7 J$