# The force applied against a moving object travelling on a linear path is given by F(x)= sinx + 2 . How much work would it take to move the object over x in [ 0, (13 pi) / 8 ] ?

Jun 5, 2017

The work is $= 10.83 J$

#### Explanation:

The work is

$\Delta W = F \Delta x$

$F = \sin x + 2$

$\Delta W = \left(\sin x + 2\right) \Delta x$

$W = {\int}_{0}^{\frac{13}{8} \pi} \left(\sin x + 2\right) \mathrm{dx}$

$= {\left[- \cos x + 2 x\right]}_{0}^{\frac{13}{8} \pi}$

$= \left(- \cos \left(\frac{13}{8} \pi\right) + \frac{13}{4} \pi\right) - \left(- \cos 0 + 0\right)$

$= \frac{13}{4} \pi + 1 - \cos \left(\frac{13}{8} \pi\right)$

$= 10.83 J$