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).
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.