How to use the work integral ∫F·dl in problems

[WahooMan]

I know the integral to compute work done is

(integral from a to b) F * dl

where F and l are vectors, but I don't understand how I would use that in a problem.

1. Are a and b moments in time?

2. What is dl? Is that the same thing as l2-l1? So would it be (integral from a to b) F(l2-l1) and just integrate that?

Any help would be greatly appreciated. Thanks.

Edit: It would really be helpful if someone could provide a sample problem and explain how to do it that way.

 

[Dale]

1) No, a and b are the starting and ending points on the path along which you want to calculate the work.
2) dl is a differential length along the path.

Here are a couple of sites with examples. The first is all 1D problems while the second has a single vector problem that it works in detail:

http://tutorial.math.lamar.edu/Classes/CalcI/Work.aspx
http://www.khanacademy.org/video/us...e-by-a-vector-field-example?playlist=Calculus

 

[paulfr]

Just remember that integration is MULTIPLICATION when one
of the factors is changing.
Since multiplication is nothing more than repeated addition,
you can see the reason for the S sigma as the symbol for integration.

With vectors it is a little more involved since directions are also must be considered
That is all