# 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, (3 pi) / 8 ] ?

Jan 14, 2016

$2.9735 J$

#### Explanation:

From precise definition of work,

$W = {\int}_{C} \vec{F} . \mathrm{dv} e c r$

So in this particular case we may reduce it to

$W = {\int}_{0}^{\frac{3 \pi}{8}} \left(\sin x + 2\right) \mathrm{dx}$

$= {\left[- \cos x + 2 x\right]}_{0}^{\frac{3 \pi}{8}}$

$= \left(- 0.3827 + \frac{6 \pi}{8}\right) - \left(- 1 + 0\right)$

$= 2.9735 J$.