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

1 Answer
Mar 29, 2016

Answer:

Approximately: #41.270 J#

Explanation:

The work done will be the integral of the force over the distance.
#W = int_1^3 F(x) dx= int_1^3 (xe^x+ 1/x) dx#
We'll leave the process of solving this integral to the student. The answer is:
#W = 2*e^3 + log(3) = 41.270 J#
Since we know that the work done is equal to the change in kinetic energy, we can say that:
#Delta KE = W = 41.270 J#