# The force applied on a moving object with a mass of 5 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 [1,4 ] ?

May 1, 2017

I got: $24 J$

#### Explanation:

As we have a variable force I would use the integral form of work as:

$W = {\int}_{{x}_{1}}^{{x}_{2}} F \left(x\right) \mathrm{dx} =$

$W = {\int}_{1}^{4} \left({x}^{2} + 1\right) \mathrm{dx} = {x}^{3} / 3 + x {|}_{1}^{4} =$
$= \left({4}^{3} / 3 + 4\right) - \left({1}^{3} / 3 + 1\right) = \frac{64 + 12 - 1 - 3}{3} = 24 J$