Question

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 ]`?

Answer 1

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`