The force applied against a moving object travelling on a linear path is given by F(x)=2x+e^x . How much work would it take to move the object over x in [1,2 ] ?

Jul 14, 2017

The work is $= 7.67 J$

Explanation:

We need

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

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

The work is

$\Delta W = F \Delta x$

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

The work is

$W = {\int}_{1}^{2} \left(2 x + {e}^{x}\right) \mathrm{dx}$

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

$= \left(4 + {e}^{2}\right) - \left(1 + e\right)$

$= 3 + {e}^{2} - e$

$= 7.67 J$