The force applied against a moving object travelling on a linear path is given by #F(x)=2x+e^x #. How much work would it take to move the object over #x in [1,2 ] #?

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Answer 1 · 2017-07-14T06:04:08

The work is #=7.67J#

We need

#inte^xdx=e^x+C#

#intx^ndx=x^(n+1)/(n+1)+C(n!=-1)#

The work is

#DeltaW=FDeltax#

#F(x)=2x+e^x#

The work is

#W=int_1^2(2x+e^x)dx#

#=[x^2+e^x]_1^2#

#=(4+e^2)-(1+e)#

#=3+e^2-e#

#=7.67J#