# 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 ] ?

Jan 7, 2016

I found $48.2 J$

#### Explanation:

Work will be given (fou our variable force) in integral form as:
$W = {\int}_{{x}_{1}}^{{x}_{2}} F \left(x\right) \mathrm{dx} = {\int}_{1}^{3} \left(2 x + x {e}^{x}\right) \mathrm{dx} =$
Let us integrate first and then substitute our extrema:

$= \int 2 x \mathrm{dx} + \int x {e}^{x} \mathrm{dx} = {x}^{2} + x {e}^{x} - {e}^{x} + c$

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

$W = \left({3}^{2} + 3 {e}^{3} - {e}^{3}\right) - \left({1}^{2} + 1 {e}^{1} - {e}^{1}\right) = 48.17 \approx 48.2 J$