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.

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).

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