The force applied against a moving object travelling on a linear path is given by #F(x)=2x+xe^x #. How much work would it take to move the object over #x in [1,3 ] #?

1 Answer
Jan 7, 2016

Answer:

I found #48.2J#

Explanation:

Work will be given (fou our variable force) in integral form as:
#W=int_(x_1)^(x_2)F(x)dx=int_1^3(2x+xe^x)dx=#
Let us integrate first and then substitute our extrema:

#=int2xdx+intxe^xdx=x^2+xe^x-e^x+c#

let us now use our extrena to solve the definite integral:

#W=(3^2+3e^3-e^3)-(1^2+1e^1-e^1)=48.17~~48.2J#