Thread: Find the work done by integral

1. Find the work done by integral

Find the work done by the force F(x) newtons along the x-axis from x=a meters to x=b meters.

F(x)= $\displaystyle x \sin (\frac{\pi * x}{4})$

I understand we need to use an integral from a to b.
What I don't understand is how to change the intervals when doing anti differentiation by parts, or if they even need to be changed at all.

Also, why do we need the integral? It seems like this is a simple F(b)-F(a) problem.

Thanks!

2. Originally Posted by Truthbetold
Find the work done by the force F(x) newtons along the x-axis from x=a meters to x=b meters.

F(x)= $\displaystyle x \sin (\frac{\pi * x}{4})$

I understand we need to use an integral from a to b.
What I don't understand is how to change the intervals when doing anti differentiation by parts, or if they even need to be changed at all.

Also, why do we need the integral? It seems like this is a simple F(b)-F(a) problem.

Thanks!
The general equation for work done by a force F given as a function of the position of the object is
$\displaystyle W = \int_a^bF(x) cos(\theta)~dx$
where $\displaystyle \theta$ is the angle between the force and the infinitesimal displacement dx. Note that in the special case where the force is constant (and $\displaystyle \theta = 0$) we get the familiar W = Fd.

$\displaystyle W = \int_{x_0}^x x~sin \left ( \frac{\pi * x}{4} \right )~cos(\theta)~dx$