# 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 [3,7] ?

Feb 13, 2016

Work=Force x distance = Fx. However, the force is changing with x (i.e. F is a function of x), so integration should be used to solve this problem. Do this and you'll find:
Work = 1181.9 J

#### Explanation:

Work=Force x distance = Fx. However, the force is changing with x (i.e. F is a function of x), so integration should be used to solve this problem. By doing this you're taking the work done over tiny (i.e. infinitesimally small) steps in x and summing them all up to get the total work.

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

To find the work done integrate F(x) between the limits 3 and 7:

Work = ${\int}_{3}^{7} {x}^{2} + {e}^{x} \mathrm{dx}$ joules

Work = ${\left[{x}^{3} / 3 + {e}^{x}\right]}_{3}^{7}$ J
Work = $\left({7}^{3} / 3 + {e}^{7}\right) - \left({3}^{3} / 3 + {e}^{3}\right)$ J
Work = ${7}^{3} / 3 + {e}^{7} - {3}^{2} - {e}^{3}$ J
Work = 1181.9 J