The force applied against an object moving horizontally on a linear path is described by F(x)=4e^x+ 1/x . By how much does the object's kinetic energy change as the object moves from x in [ 1, 3 ]?

1 Answer
Jul 16, 2017

The change in kinetic energy is =70.57Jf

Explanation:

We need

inte^xdx=e^x+C

int(1/x)dx=ln(|x|)+C

The change in Kinetic Energy is equal to the work done.

DeltaE=W=F*d

W=int_1^3(4e^x+1/x)dx

=[4e^x+lnx]_1^3

=(4e^3+ln3)-(4e+ln1)

=70.57J