unfortunately, info on google gets lost in all the ads. always give yahoo a try.

edit – also, sometimes it is the way you ask. i just searched for "how does a hair dryer work" and got this on the first try.

good luck with the project.

A definite integral is defined (ignoring signs for the moment) as the area under a given function and above the x axis between points a and b. So we have a geometry problem: find the area.
The trick of calculus is, get a rough answer, then improve it, then improve that, etc, until you take a limit and get the perfect answer.
The first rough answer is to chop the interval [a,b] into slices (subintervals) and put a rectangle on top of each using it as the base width. Now, how tall do we make the rectangle? It matters in the rough answers, but turns out not to matter in the limit. So suppose we use the Left Hand Sum rule: on the left side of the interval, go up until you hit the function: use that as the height.
Now you have a lot of rectangles that mostly cover the area, but might be too tall or too short in spots. If for example you have an increasing function (one that goes up to the right) then all these left hand rectangles will be too short. That's okay. We're going to improve on it.
Now we take the intervals and cut them up smaller, making thinner rectangles but more of them. We adjust the heights of the new rectangles the same way, and we still have an error, but it is smaller.

So that's the master plan. We are adding up "lots" of rectangles, and letting the number n of rectangles go to infinity. Our guess for the integral is the area of the rectangles, which is the sum of all the areas of the individual rectangles, which is the sum from 1 to n of the height times width. If you cut up the interval evenly, then each width is (b-a)/n, but that's not required–you only have to make sure that none of the intervals stay big as you chop them up finer and finer. The height is f(x), or rather f(x*), where x* is the point on the left edge. Or you could use the right edge, or the middle, or other options.

I hope that helps.

Permalink: Bluetooth 4.0 has new features from Ubergizmo | RSS Sponsor: Win a Fellowes Microshred Paper Shredder!