# The force applied against a moving object travelling on a linear path is given by F(x)= x^2+3e^x. How much work would it take to move the object over x in [0,2] ?

Dec 7, 2017

The answer is $= 21.83 J$

#### Explanation:

The force is given by

$F \left(x\right) = {x}^{2} + 3 {e}^{x}$

The work $W$ is the force multiplied by the distance.

Therefore,

The work is

$\mathrm{dW} = F \left(x\right) \mathrm{dx}$

So,

$W = {\int}_{0}^{2} \left({x}^{2} + 3 {e}^{x}\right) \mathrm{dx}$

$= {\left[\frac{1}{3} {x}^{3} + 3 {e}^{x}\right]}_{0}^{2}$

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

$= 21.83 J$