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

Chang in KE = work done against force=${\int}_{1}^{3} F \left(x\right) \mathrm{dx}$
$= {\int}_{1}^{3} \left(x + 2\right) \mathrm{dx} = {\left[{x}^{2} / 2 + 2 x\right]}_{1}^{3}$
$= {3}^{2} / 2 + 2 \times 3 - {1}^{2} / 2 - 2 \times 1 = 8 J$