What does the big F stand for?


by Line
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Line
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#1
May10-06, 01:41 AM
P: 218
What does the big F stand for in eqautions like

f(x)-sinb=F(a)-F(b) ??

It's not like the little f in function.
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bomba923
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#2
May10-06, 02:52 AM
P: 736
Typically, textbooks discussing the Fundamental Theorem of Calculus
refer to F(x) ("big F") as the antiderivative of f(x) ("little f").

*This link might help
HallsofIvy
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#3
May11-06, 11:35 AM
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"f(x)-sinb=F(a)-F(b)" makes no sense. Are you sure it wasn't something like [itex]\int_b^a f(x)dx= F(a)- F(b)[/itex]?

Line
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#4
May11-06, 07:24 PM
P: 218

What does the big F stand for?


SO a capital F means the antiderivative of a function?
Hurkyl
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#5
May11-06, 07:25 PM
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By convention, if we use a lower-case letter to denote a function, we use an upper-case letter to denote its anti-derivative.

It's not something you have to do -- it's just something that people usually do because everyone else does it and it's convenient.
mathwonk
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#6
May11-06, 08:51 PM
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according to some bumper stickers i have seen, it stands for the president.
HallsofIvy
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#7
May26-06, 06:22 AM
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With "_ _ _" after it?
moose
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#8
May26-06, 11:34 PM
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I've seen this used as follows
f(x)=x^2
g(x)=x/2
F(x)=f(x)/(g(x)

Other than that, doesn't ring a bell.

EDIT: What math class did you see this in?
Theelectricchild
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#9
May30-06, 11:18 PM
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Did you mean to type anything else? I didn't see a closed parenthesis. If it is indeed so, then the F(x) you saw does not refer to any antiderivative, but simply f(x) / g(x). As Hurkyl said below, the antiderivative notation is simply convention, and not a strict rule of mathematics.
HallsofIvy
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#10
May31-06, 06:51 AM
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Quote Quote by moose
I've seen this used as follows
f(x)=x^2
g(x)=x/2
F(x)=f(x)/g(x)

Other than that, doesn't ring a bell.

EDIT: What math class did you see this in?
That is simply defining F(x) to be f(x)/g(x)- making it clear that the convention "F(x) is an anti-derivative of f(x)" is not being used!
arildno
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#11
May31-06, 10:05 AM
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Actually, I hereby declare that the following definition of F(x) is unique and unviolable:
[tex]F(x)=\frac{\pi}{1+\frac{\pi}{1+\frac{x}{e+\pi}}}[/tex]


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