# The force applied on a moving object with a mass of 3 kg  on a linear path is given by F(x)=x^2+1 . How much work would it take to move the object over x in [0,2 ] ?

Jan 22, 2017

I found: $W = \frac{14}{3} J$

#### Explanation:

Having a variable force I would use the work in integral form as:
$W = {\int}_{{x}_{1}}^{{x}_{2}} F \left(x\right) \mathrm{dx}$ along $x$.
We have:
$W = {\int}_{0}^{2} \left({x}^{2} + 1\right) \mathrm{dx} =$
Solve it as usual:
$= {\int}_{0}^{2} \left({x}^{2} + 1\right) \mathrm{dx} = {x}^{3} / 3 + x =$
Apply the extremes:
$= \left({2}^{3} / 3 + 2\right) - \left({0}^{3} / 3 + 0\right) = \frac{8}{3} + 3 = \frac{8 + 6}{3} = \frac{14}{3}$
so we get:
$W = \frac{14}{3} J$