# The force applied against an object moving horizontally on a linear path is described by F(x)=x^2+ 5 . By how much does the object's kinetic energy change as the object moves from  x in [ 1, 2 ]?

Aug 9, 2017

The change in kinetic energy is $= 7.33 J$

#### Explanation:

We need

$\int {x}^{n} \mathrm{dx} = {x}^{n + 1} / \left(n + 1\right) + C \left(n \ne - 1\right)$

The change in kinetic energy is equal to the work.

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

Therefore,

$W = {\int}_{1}^{2} \left({x}^{2} + 5\right) \mathrm{dx}$

$= {\left[{x}^{3} / 3 + 5 x\right]}_{1}^{2}$

$= \left(\frac{8}{3} + 10\right) - \left(\frac{1}{3} + 5\right)$

$= 5 + \frac{7}{3}$

$= 7.33 J$