# Using Simpson's rule to find the work done on an object

• Apr 29th 2013, 05:45 PM
Steelers72
Using Simpson's rule to find the work done on an object
The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use Simpson's Rule to estimate the work done by the force in moving an object a distance of 18 m.
 x 0 3 6 9 12 15 18 f(x) 9.5 9.4 8.4 8 7.9 7.5 7.3

S= deltax/3[f(x)+4f(x)+2f(x)+4f(x)+...f(x)]

3/3[9.5+4(9.4)+2(8.4)+4(8)+2(7.9)+4(7.5)+7.3]

S=149

How do I relate this to finding the work done?

I thought maybe I could take integral from 0 to 18 of 149xdx and I got 24138 as an answer, which is wrong. Am I making a silly error? Thanks for any help.
• Apr 29th 2013, 10:45 PM
chiro
Re: Using Simpson's rule to find the work done on an object
Hey Steelers72.

The work done is the force applied over some distance. In this particular case it will be the integral over the path (which is the x direction vector).
• May 1st 2013, 12:02 PM
emakarov
Re: Using Simpson's rule to find the work done on an object
Quote:

Originally Posted by Steelers72
How do I relate this to finding the work

The work, by definition, is $\displaystyle \int_0^{18}f(x)\,dx$, of which S found using the Simpson's rule is an approximation