The force applied against an object moving horizontally on a linear path is described by #F(x)= cospix+x #. By how much does the object's kinetic energy change as the object moves from # x in [ 0, 2 ]#?
We can use the Work-K.E. theorem that tells us that:
or that work done on the system is equal to the change in kinetic energy.
Here we need to evaluate the work of a variable force so we use the integral version of work as: