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

Mar 13, 2018

$\text{35 Joule}$

Explanation:

Small work done by force for a small distance $\mathrm{dx}$ is given by

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

Total work done is

$W = \int \mathrm{dW} = \int F . \mathrm{dx}$

$W = {\int}_{2}^{3} \left(2 {x}^{3} + x\right) \mathrm{dx}$

$W = {\left[\frac{2 {x}^{4}}{4} + {x}^{2} / 2\right]}_{2}^{3}$

$W = {\left[{x}^{4} / 2 + {x}^{2} / 2\right]}_{2}^{3}$

$W = \frac{1}{2} {\left[{x}^{4} + {x}^{2}\right]}_{2}^{3}$

$W = \frac{1}{2} \left[\left({3}^{4} - {2}^{4}\right) + \left({3}^{2} - {2}^{2}\right)\right] = \text{35 Joule}$