



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 
