# 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,pi/3] ?

Mar 25, 2016

$\frac{1}{2} + 2 \cdot \frac{\pi}{3}$ Joules

#### Explanation:

The work necessary is $\mathrm{dW} = F \left(x\right) \cdot \mathrm{dx}$

as the movement is between 0 and 3 metres

$W = {\int}_{0}^{3} F \left(x\right) \mathrm{dx} = {\int}_{0}^{3} \left(s e n x + 2\right) \mathrm{dx} = \frac{1}{2} + 2 \cdot \frac{\pi}{3}$ due to

$\cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$