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

Apr 16, 2016

$\left(3 + {e}^{2}\right)$ units

#### Explanation:

Work done
Let the object move a distance $\mathrm{dx}$.
Work done $\mathrm{dw} = - F \left(x\right) . \mathrm{dx}$
$- v e$ sign shows that force is being applied against the direction of motion. Total work done is integral of the expression within the stated limits.

$w = - {\int}_{0}^{2} F \left(x\right) . \mathrm{dx} = - {\int}_{0}^{2} \left(2 + {e}^{x}\right) \mathrm{dx}$
$= - {\left[2 x + {e}^{x}\right]}_{0}^{2} = - \left[\left(2 \times 2 + {e}^{2}\right) - \left(2 \times 0 + {e}^{0}\right)\right]$
$= - \left[\left(4 + {e}^{2}\right) - \left(1\right)\right]$
$= - \left(3 + {e}^{2}\right)$
Work done in moving the object$= 3 + {e}^{2}$