Posted on 12/26/2005 2:10:31 PM PST by the_red_anedote
Edited on 12/26/2005 2:21:13 PM PST by Admin Moderator. [history]
China will never go down, and don't think you can banish communism. Because the people won't let it. They know they are the last standing, they are the only ones left. America is in a decline while China's climaxing, America will go down. We are just done with our prime, if anything, we were going into a depression since 1992 (and don't say you don't know that year). Communism is the American's medias' worst nightmare, because of censorship. I hope we all have to read one newspaper and wipe my butt with one brand of tiolet paper. I hope we all die for our next generations to wear the red armband. We deserved 9/11, and they enjoyed it. You probably hate me now, I know, you just still think like its 1945, well too bad its 2005. We only stand to fall.
I look at it more as, "Yes, it ends, but we have now. So let's have a blast while we last."
Meanwhile, California is doing the "flood" thing again. Hard rain all night, and continuing.
Howya Das!!
Boring. I want it to do the "earthquake" thing.
It is approved!
Would you settle for a psunami?
A psunami? Is it anything like a Tsunami?
It's caused by a big whale with ptsneumonia.
With a pstrneumatic pstump....
Tsunami sounds more like it : )
Sheeeeeeeeeeeeeeeeeeeeeeesh !
LOL
R O T F L M A O
I wouldn't mind a Tsunami... I could stand on Croagh Patrick and watch it wipe out Westport....
HEHE.
And eat dessert first, because life is short.
I think about this too. We have fire, and we have ash. The ash seems obvious enough, and we treat it with respect, but where does the fire go?
It may be the difference between Quantum Mechanics and Newtonian Physics, but it seems intuitively obvious that the fire, or spirit, does not utterly disappear. Where it does go may remain, as it always has been, a lifelong mystery.
Okay...............Sue Nami it is!!
I'm going to sue Nami....
Calculus and Analysis Calculus Integrals
MathWorld Contributors Cortzen
Integral
An integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the fundamental objects of calculus. Other words for integral include antiderivative and primitive. The Riemann integral is the simplest integral definition and the only one usually encountered in physics and elementary calculus. In fact, according to Jeffreys and Jeffreys (1988, p. 29), "it appears that cases where these methods [i.e., generalizations of the Riemann integral] are applicable and Riemann's [definition of the integral] is not are too rare in physics to repay the extra difficulty."
The Riemann integral of the function over from to is written
(1)
Note that if , the integral is written simply
(2)
as opposed to .
Every definition of an integral is based on a particular measure. For instance, the Riemann integral is based on Jordan measure, and the Lebesgue integral is based on Lebesgue measure. The process of computing an integral is called integration (a more archaic term for integration is quadrature), and the approximate computation of an integral is termed numerical integration.
There are two classes of (Riemann) integrals: definite integrals such as (ž), which have upper and lower limits, and indefinite integrals, such as
(3)
which are written without limits. The first fundamental theorem of calculus allows definite integrals to be computed in terms of indefinite integrals, since if is the indefinite integral for , then
(4)
Since the derivative of a constant is zero, indefinite integrals are defined only up to an arbitrary constant of integration , i.e.,
(5)
Wolfram Research maintains a web site http://integrals.wolfram.com/ that can find the indefinite integral of many common (and not so common) functions.
Differentiating integrals leads to some useful and powerful identities. For instance, if is continuous, then
(6)
which is the first fundamental theorem of calculus. Other derivative-integral identities include
(7)
the Leibniz integral rule
(8)
(Kaplan 1992, p. 275), its generalization
(9)
(Kaplan 1992, p. 258), and
(10)
as can be seen by applying (ž) on the left side of (ž) and using partial integration.
Other integral identities include
(11)
(12)
(13)
(14)
and the amusing integral identity
SO THERE!
Nami is in Tokyo. I will give her the bad news.
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