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

Nov 7, 2016

The work $= \frac{25}{2} + {e}^{3}$

#### Explanation:

The work done = force*distance
The unit work $\mathrm{dW} = F \left(x\right) \cdot \mathrm{dx}$
$\therefore \mathrm{dW} = \left(3 x + {e}^{x}\right) \mathrm{dx}$
$W = {\int}_{0}^{3} \left(3 x + {e}^{x}\right) \mathrm{dx} = {\left[\frac{3 {x}^{2}}{2} + {e}^{x}\right]}_{0}^{3}$
$= \left(\frac{27}{2} + {e}^{3} - {e}^{0}\right)$
$= \frac{25}{2} + {e}^{3}$