# The force applied on a moving object with a mass of 2 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 ] ?

Jan 10, 2016

24 units

#### Explanation:

Because force is a function of $x$ we write:

$W = {\int}_{1}^{4} F . \mathrm{dx}$

$\therefore W = {\int}_{1}^{4} \left({x}^{2} + 1\right) . \mathrm{dx}$

$W = {\left[{x}^{3} / 3 + x\right]}_{1}^{4}$

$W = \left[\frac{64}{3} + 4\right] - \left[\frac{1}{3} + 1\right]$

$W = \frac{76}{3} - \frac{4}{3} = \frac{72}{3} = 24 \text{units}$

No units for distance are given. If it were metres then the answer would be in Joules.