# What's this symbol stand for?

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 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?
 P: 1,076 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)
 P: 218 And just what is an integral?
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P: 7,272

## What's this symbol stand for?

I find it interesting that you know enough to post this question in the calculus section?? Hmmm??
 Sci Advisor HW Helper P: 3,149 Incidentally, the $\int$ symbol originated as an elongated letter "S" and stood for "sum."
P: 1,017
 Quote by Line And just what is an integral?
A derivative of a function is the rate of change of that function as some other variable changes. For instance, the velocity of an object is the rate of change of position with time. You can determine this to arbitrary accuracy by taking intervals of distance travelled ($$\Delta x$$) and divide by the time taken ($$\Delta t$$):

$$v = \frac{\Delta x}{\Delta t}$$

The larger the interval $$\Delta x$$ taken, the larger the interval $$\Delta t$$ is. Also, the less accurate the value of the velocity at time t will be, since any changes in velocity during $$\Delta t$$ 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 $$\Delta x$$ 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 anti-derivate - it will undo the derivative to give you the original function, so:

$$\int v(t) dt = \int f'(t) dt = f(t)$$
 P: 218 You must be an american. Americans give long complicated answers to things.
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 Quote by Line You must be an american. Americans give long complicated answers to things.
As opposed to short, simple, wrong answers?
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,706 My father used to call the $$\int$$ symbol a "seahorse"!
 P: 789 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.
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 Quote by Line You must be an american. Americans give long complicated answers to things.
With that attitude, you'll make very far in life.

Personally, I always thought Americans gave short lazy answers.
 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.
 Emeritus Sci Advisor PF Gold P: 4,921 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.
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 Quote by Math Is Hard Calculus will teach you patience. Either you will learn patience or your 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.

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
 Sci Advisor P: 1,132 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.
 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.
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