# 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 [2, 3 ] ?

Jan 5, 2018

The work is $= 20.2 J$

#### Explanation:

The equation is

$\text{Work"="Force"xx"distance}$

Here,

The force is $F \left(x\right) = 3 x + {e}^{x}$

Therefore,

$\Delta W = F \times \Delta x$

$\mathrm{dW} = \left(3 x + {e}^{x}\right) \mathrm{dx}$

Integrating both sides

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

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

$= \left(\frac{27}{2} + {e}^{3}\right) - \left(6 + {e}^{2}\right)$

$= \frac{15}{2} + {e}^{3} - {e}^{2}$

$= 20.2 J$