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

Nov 21, 2016

I found: $27.9 J$

#### Explanation:

Here you have a variable force so we need to use the integral form of the work as:
$W = {\int}_{{x}_{1}}^{{x}_{2}} F \left(x\right) \mathrm{dx}$
$W = {\int}_{2}^{3} \left(x + 2 {e}^{x}\right) \mathrm{dx} =$
$= {x}^{2} / 2 + 2 {e}^{x}$ evaluated between $x = 2$ and $x = 3$
$= \left({3}^{2} / 2 + 2 {e}^{3}\right) - \left({2}^{2} / 2 + 2 {e}^{2}\right) = 27.9 J$