The force applied against a moving object travelling on a linear path is given by #F(x)=2+e^x #. How much work would it take to move the object over #x in [0,2 ] #?

1 Answer
Apr 16, 2016

Answer:

#(3+e^2)# units

Explanation:

Work done
Let the object move a distance #dx#.
Work done #dw=-F(x).dx#
#-ve# sign shows that force is being applied against the direction of motion. Total work done is integral of the expression within the stated limits.

#w=-int_0^2F(x).dx=-int_0^2(2+e^x)dx#
#=-[2x+e^x]_0^2=-[(2xx2+e^2)-(2xx0+e^0)]#
#=-[(4+e^2)-(1)]#
#=-(3+e^2)#
Work done in moving the object#=3+e^2#