# The force applied against an object moving horizontally on a linear path is described by F(x)=x^2-x+2 . By how much does the object's kinetic energy change as the object moves from  x in [ 1, 3 ]?

Oct 18, 2016

The work is done is, so it's KE increases by, $\frac{26}{3}$ J
$W = {\int}_{a}^{c} F \left(x\right) \mathrm{dx}$
$= {\int}_{1}^{3} {x}^{2} - x + 2 \mathrm{dx}$
$= {\left[{x}^{3} / 3 - {x}^{2} / 2 + 2 x\right]}_{1}^{3} = \frac{26}{3}$J