David Fontaine <dav### [at] faricynet> wrote in message
news:3887B189.DE2796FE@faricy.net...
> I am just wondering, what exactly does integration do? Several people have
tried
> unsuccessfully to explain it to me. I believe something to do with area
under a
> curve? Just tell me what the input represents and what the output
represents,
> that's all I really want to know.

input: a bunch of things to be added up, with a certain weight for each.
An example is the average. You add up all of them but weight
them by 1/(number of things).  average of a, b, and c is
a/3 +b/3+c/3.
Usually the term 'integration' is used when the things to
be added for a continuum of values. Thats why integration is
considered 'calculus'.
Say you want to know how a planet is going to revolve around its sun.
The force of gravity on the planet is not usually constant because the
planet
can go from one distance from its sun to other distances. To find out where
it will be tomorrow, you could 'move' it (on paper) in little increments
calculating the forces on it anew for each second, using its new position
and new forces. You are actually adding up all these effects, second
after second. But since it is more accurate to consider time as a
continuum, you really should add up a continuum of miniscule
effects. That is, you 'integrate' the effects

output: the sum

oh yeah, 'the area under the curve' explanation comes from finding the
area under a curve by adding up a bunch of rectangular regions (for
which you know that area=length X width) areas

Post a reply to this message