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

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Answer 1 · 2018-01-05T10:48:10

The work is #=20.2J#

The equation is

#"Work"="Force"xx"distance"#

Here,

The force is #F(x)=3x+e^x#

Therefore,

#DeltaW=FxxDeltax#

#dW=(3x+e^x)dx#

Integrating both sides

#W=int_2^3(3x+e^x)dx#

#=[3/2x^2+e^x]_2^3#

#=(27/2+e^3)-(6+e^2)#

#=15/2+e^3-e^2#

#=20.2J#