# The force applied against a moving object travelling on a linear path is given by F(x)= x^2+e^x . How much work would it take to move the object over x in [2, 5] ?

Aug 3, 2017

The work is $= 180.02 J$

#### Explanation:

$\int {e}^{x} \mathrm{dx} = {e}^{x} + C$

$\int \left({x}^{n}\right) \mathrm{dx} = {x}^{n + 1} / \left(n + 1\right) + C \left(n \ne - 1\right)$

The work is

$\Delta W = F \left(x\right) \cdot \Delta x$

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

$W = {\int}_{2}^{5} \left({x}^{2} + {e}^{x}\right) \mathrm{dx}$

$= {\left[\frac{1}{3} {x}^{3} + {e}^{x}\right]}_{2}^{5}$

$= \left(\frac{1}{3} \cdot {5}^{3} + {e}^{5}\right) - \left(\frac{1}{3} \cdot {2}^{3} + {e}^{2}\right)$

$= \frac{125}{3} - \frac{8}{3} + {e}^{5} - {e}^{2}$

$= \frac{117}{3} + 141.02$

$= 180.02 J$