The force applied against a moving object travelling on a linear path is given by #F(x)=xe^x #. How much work would it take to move the object over #x in [2, 4] #?

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Answer 1 · 2016-07-20T21:22:32

#=e^2 (3 e^2 - 1) #

in one dimension:

#W = int_a^b \ F(x) \ dx#

#= int_2^4 \ x e^x \ dx#

#= int_2^4 \ x d/dx( e^x) \ dx#

and so by IBP

#=[x e^x]_2^4 - int_2^4 \ d/dx (x) e^x \ dx#

#=[x e^x]_2^4 - int_2^4 \ e^x \ dx#

#=[(x-1) e^x]_2^4 #

#=3 e^4 - e^2 #

#=e^2 (3 e^2 - 1) #