The force applied against an object moving horizontally on a linear path is described by #F(x)=x^2+ x-1 #. By how much does the object's kinetic energy change as the object moves from # x in [ 1, 2 ]#?
Work done = force x distance moved in the direction of the force.
Because the force applied is a function of distance we get:
This work will appear as an increase in kinetic energy.