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

Oct 9, 2016

I found $6.7 J$

#### Explanation:

I think we would need at least an equal force to keep on moving the object as the one opposing it (at least without accelerating it maintaining a constant velocity)..
Here we have a variable force (depending on $x$) so we need to use the integral form for Work as:
$W = {\int}_{{x}_{1}}^{{x}_{2}} F \left(x\right) \mathrm{dx}$
or in our case:
$W = {\int}_{1}^{2} \left(2 + {e}^{x}\right) \mathrm{dx} =$
let us solve it:
$W = 2 x + {e}^{x}$ evaluated between $1 \mathmr{and} 2$ gives us:
$W = \left(4 + {e}^{2}\right) - \left(2 + e\right) = 2 + {e}^{2} - e = 2 + e \left(e - 1\right) = 6.67 \approx 6.7 J$