# The force applied against a moving object travelling on a linear path is given by F(x)= 2x^3+6x. How much work would it take to move the object over x in [2, 3] ?

Jan 28, 2016

$W = 47.5 J$

#### Explanation:

Work, is an integral of force over distance, that is
$W = \setminus \int F \left(x\right) \mathrm{dx}$

Here, $F \left(x\right) = 2 {x}^{3} + 6 x$
So, integrating $F \left(x\right)$ with respect to $x$ from $2$ to $3$,
${\int}_{2}^{3} F \left(x\right) \mathrm{dx} = \setminus {\int}_{2}^{3} \left(2 {x}^{3} + 6 x\right) \mathrm{dx} = \left(\setminus \frac{2 {x}^{4}}{4} + \setminus \frac{6 {x}^{2}}{2}\right) {|}_{2}^{3} = \setminus \frac{{3}^{4} - {2}^{4}}{2} + 3 \left({3}^{2} - {2}^{2}\right)$

Solving the above equation gives you the answer provided above.