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Remember the integral of X 2? |
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| If we want the area between X 2 and the X axis from 0 to 1, | ||
| like we just did on the last page, we have ... | ||
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| SEE A PATTERN????? | ||
| Through lots of math hocus pocus, Newton, Leibnitz and friends | ||
| came up with a little shortcut for doing all this summing. | ||
| Hey, they knew that computers wouldn't be invented for 300 years, | ||
| and they were tired of doing all that summing too! | ||
| Our friend the integral was the answer. | ||
| These guys found: | ||
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| This little bit of insight is called: | ||
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THE FUNDAMENTAL THEOREM |
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OF INTEGRAL CALCULUS |
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| Sounds pretty important, eh??? | ||
| IT IS!!! | ||
| Wow, what a lifesaver. | ||
| That old summing thing would have gotten to be a real drag. | ||
| Now, if we want to figure out the area between F(x) = X 2 and the X axis, | ||
| we can do it! | ||
| And still have time left to do something else today too! | ||
| But there's more to add to this. | ||
| Otherwise, there would be no next button at the top of the page! | ||
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copyright 2005 Bruce Kirkpatrick |
