Calculus The Fundamental Theorem of Calculus
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The Big Area Shortcut
The Fundamental Theorem of Calculus

 

 Remember the integral of X 2?

 

 
 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 ...

 

 
 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:

 

 
 This little bit of insight is called:
 

 THE FUNDAMENTAL THEOREM

 OF INTEGRAL CALCULUS

 
 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!
 

   copyright 2005 Bruce Kirkpatrick

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