# 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, (5pi) / 3 ] ?

Jul 5, 2017

The work is=5.74J

#### Explanation:

We need

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

The work done is

$W = F \cdot d$

The work done is

$W = {\int}_{0}^{\frac{5}{3} \pi} \left(1 + \sin x\right) \mathrm{dx}$

$= {\left[x - \cos x\right]}_{0}^{\frac{5}{3} \pi}$

=(5/3pi-cos(5/3pi))-(0-cos0))#

$= \left(\frac{5}{3} \pi + 1 - 0.5\right)$

$= 5.74 J$