The force applied against a moving object travelling on a linear path is given by #F(x)=x+2e^x #. How much work would it take to move the object over #x in [2, 3] #?

1 Answer
Nov 21, 2016

Answer:

I found: #27.9J#

Explanation:

Here you have a variable force so we need to use the integral form of the work as:
#W=int_(x_1)^(x_2)F(x)dx#
in your case:
#W=int_2^3(x+2e^x)dx=#
#=x^2/2+2e^x# evaluated between #x=2# and #x=3#
#=(3^2/2+2e^3)-(2^2/2+2e^2)=27.9J#