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

Apr 10, 2017

21.5 J

#### Explanation:

work done = $f \cdot \mathrm{dx}$
here F=$3 \cdot {x}^{2} + x$
substituting and integrating from 2 to 3 we get
W=${\int}_{2}^{3} \left(3 {x}^{2} + x\right) . \mathrm{dx}$
w=${\left[{x}^{3} + {x}^{2} / 2\right]}_{2}^{3}$
$\left[27 + \frac{9}{2}\right] - \left[8 + \frac{4}{2}\right]$
$19 + \frac{5}{2}$
$\frac{43}{2}$=$21.5 J$