The force applied against a moving object travelling on a linear path is given by #F(x)= x^2+3e^x#. How much work would it take to move the object over #x in [0,2] #?

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Answer 1 · 2017-12-07T07:03:37

The answer is #=21.83J#

The force is given by

#F(x)=x^2+3e^x#

The work #W# is the force multiplied by the distance.

Therefore,

The work is

#dW=F(x)dx#

So,

#W=int_0^2(x^2+3e^x)dx#

#=[1/3x^3+3e^x]_0^2#

#=(8/3+3e^2)-(0+3e^0)#

#=21.83J#