The force applied against a moving object travelling on a linear path is given by F(x)= 4x + 4. How much work would it take to move the object over x in [ 1, 5] ?

Mar 24, 2016

$64$ units.

Explanation:

Work done = force x distance moved in the direction of the force.

Since the force $F$ is a function of the displacement $x$ we need to use integration:

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

$\therefore W = {\int}_{1}^{5} \left(4 x + 4\right) . \mathrm{dx}$

$\therefore W = {\left[\frac{4 {x}^{2}}{2} + 4 x\right]}_{1}^{5}$

$W = {\left[2 {x}^{2} + 4 x\right]}_{1}^{5}$

$W = \left[50 + 20\right] - \left[2 + 4\right] = 70 - 6 = 64$