# The force applied against a moving object travelling on a linear path is given by F(x)= sinx + 1 . How much work would it take to move the object over x in [ 0,pi/8 ] ?

Jun 22, 2017

The work is $= 0.469 J$

#### Explanation:

We need

$\int \sin x \mathrm{dx} = - \cos x$

The work done is

$W = F \cdot d$

The force is $F = 1 + \sin x$

The work done is

$W = {\int}_{0}^{\frac{1}{8} \pi} \left(1 + \sin x\right) \mathrm{dx}$

$= {\left[x - \cos x\right]}_{0}^{\frac{1}{8} \pi}$

$= \left(\frac{1}{8} \pi - \cos \left(\frac{\pi}{8}\right)\right) - \left(0 - \cos 0\right)$

$= \left(\frac{1}{8} \pi - 0.92 + 1\right)$

$= \left(\frac{1}{8} \pi + 0.08\right)$

$= 0.469 J$