# 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) / 2 ] ?

Jul 26, 2017

I got $8.85 J$

#### Explanation:

Here the force depends upon the displacement $x$ so we need to evaluate the Work in integral form.
We have that:

$\mathrm{dW} = F \left(x\right) \mathrm{dx}$ that represents a very small (infinitesimal) work.

To find the complete Work we integrate to get:

$W = {\int}_{0}^{5 \frac{\pi}{2}} F \left(x\right) \mathrm{dx} = {\int}_{0}^{5 \frac{\pi}{2}} \left[\sin \left(x\right) + 1\right] \mathrm{dx} = - \cos \left(x\right) + x {|}_{0}^{5 \frac{\pi}{2}} =$

We use the Fundamental Theorem of Calculus and get:

$= \left[- \cos \left(5 \frac{\pi}{2}\right) + 5 \frac{\pi}{2}\right] - \left[- \cos \left(0\right) + 0\right] = 0 + 5 \frac{\pi}{2} + 1 - 0 = \frac{5}{2} \left(3.14\right) + 1 = 8.85 J$