Integrals are essentially used to get areas under curves.

If you've done Reimann sums yet, you know that you can cut sections of the curve into a bunch of rectangles, multiply the bases (Delta X) together with the heights (Y values), and approximate the area under the curve. Well with integrals, you do the same thing, except the you take the limit of Delta X as it approaches zero (turning it into dx: a very, very small distance). This time though, the area under the curve is (practically) exact.

There are three parts to the basic integral. That fatass "S" thing in front is known as Sigma, and basically tells you to add. Following that, there's the f(x) equation (the "height" of the rectangles). Finally, there's dx (the infinitesmally small "width" of the rectangles). So the Sigma up in front tells you to add all the little areas of dx*f(x) together.

It might sound convoluted at first, but it'll eventually click. You're going to really love calc II next year, when they try to tell you that 1 the the infinite power is fricking 2.718. Now THAT'S convoluted. (1x1x1x1x1x1... = ...2?)

As for integral applications, you'll eventually use them to figure out how long curves actually are, or to find a path equation for an electron in particle physics. Pretty much every physical science field uses integrals in some way or another. They're pretty integral (AHAHAHAHAHAha...ha...haah...) to physics jobs.

Last Edit: March 06, 2009, 03:06:28 am by Juris

"I would be totally embarassed to write this, even as a fakepost. it's not funny except in how you seem to think it's good. look at all the redundancies, for fuck's sake. "insipid semantics, despicable mediocrity" ugh gross gross. I want to take a shower every time I read your prose." -Steel