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 [0,2 ] ?

May 4, 2017

The work is $= 4.67 J$

Explanation:

The work is

work= force * distance

$\mathrm{dW} = F \mathrm{dx}$

$\mathrm{dW} = \left({x}^{2} + 1\right) \mathrm{dx}$

$W = {\int}_{0}^{2} \left({x}^{2} + 1\right) \mathrm{dx}$

$= {\left[{x}^{3} / 3 + x\right]}_{0}^{2}$

$= \left(\frac{8}{3} + 2\right) - \left(0\right)$

$= \frac{14}{3}$

$= 4.67 J$