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What's this symbol stand for? 
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#1
Dec1305, 12:37 AM

P: 218

In Calculus what's that big symbol that's before a function stand for. I kinda looks like a big long f.
And then there's that qoutation mark looking thing. It appears beside the F in a function. It kinda looks like this.....F'.....what's it mean? 


#2
Dec1305, 12:47 AM

P: 1,075

The f looking symbol you refer to that appears before a function is called an integral.
and about the quotation mark thing '. if f(x) is a function then f'(x) read f prime of x is the derivative of f(x) 


#3
Dec1305, 01:30 AM

P: 218

And just what is an integral?



#4
Dec1305, 01:59 AM

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What's this symbol stand for?
I find it interesting that you know enough to post this question in the calculus section?? Hmmm??



#5
Dec1305, 03:13 AM

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Incidentally, the [itex]\int[/itex] symbol originated as an elongated letter "S" and stood for "sum."



#6
Dec1305, 04:09 AM

P: 1,017

[tex]v = \frac{\Delta x}{\Delta t}[/tex] The larger the interval [tex]\Delta x[/tex] taken, the larger the interval [tex]\Delta t[/tex] is. Also, the less accurate the value of the velocity at time t will be, since any changes in velocity during [tex]\Delta t[/tex] will effect the value you get. But as the intervals get smaller and smaller, the value for the velocity you get for that interval of time becomes more accurate. As [tex]\Delta x[/tex] tends towards zero, then, the value for the velocity at time t becomes correct. A derivative of a function does just this, so if the function of position at some time t is f(t) then the derivate will give you velocity as a function of time: v(t) = f'(t). An integral is an antiderivate  it will undo the derivative to give you the original function, so: [tex]\int v(t) dt = \int f'(t) dt = f(t)[/tex] 


#7
Dec1305, 06:09 PM

P: 218

You must be an american. Americans give long complicated answers to things.



#8
Dec1305, 06:41 PM

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#9
Dec1305, 06:41 PM

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My father used to call the [tex]\int[/tex] symbol a "seahorse"!



#10
Dec1305, 06:42 PM

P: 787

Agreed. The response wasn't even that long. If you'd like to read a real solid definition of the integral and understand all parts of it, get ready to read over 100 pages of material.



#11
Dec1305, 08:30 PM

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Personally, I always thought Americans gave short lazy answers. 


#12
Dec1305, 10:32 PM

P: 218

The Japanese know how to keep it real short. Did you know that they found a reason that american kids aren't doing better. The books are so darned thick. Compared to countries like Germany and Japan which score higher our books are extremly thick. Seems the answer is to keep it short and to the point. Through having less words you cover more material and not just lalalala. They also found that the other countries have more diagrams in their textbooks and we don't.



#13
Dec1305, 11:33 PM

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Calculus will teach you patience. Either you will learn patience or you will not survive into further mathematics courses. You can't expect a 12 week (or longer) course to be summarized into a couple of short sentences. El Hombre did a great job distilling a large amount of information into a condensed form for you.



#14
Dec1305, 11:41 PM

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Actually thats exactly what they do in Real Analysis  at one point they just summarize your entire 2 classes of Calculus into a few equations and you end up with a nice expression on your face 


#15
Dec1305, 11:56 PM

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Most of the time you can find alot of nice webpages online from universities, covering all kinds of topics, that are very to the point, so you have some options, that's what i do when a book is very bad.
I'm pretty sure though it's not really because of how thick the books are that people don't do very well, that's just a lame excuse in my opinion. 


#16
Dec1405, 12:04 AM

P: 11

Also, basic courses are pretty much the same in every university in the world, and i bet you every good mathematitian, no matter where in the world was born or formed ,has read the classical texts.



#17
Dec1405, 12:16 AM

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