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What does the big F stand for?by Line
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#1
May1006, 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. 


#2
May1006, 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 


#3
May1106, 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]?



#4
May1106, 07:24 PM

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What does the big F stand for?
SO a capital F means the antiderivative of a function?



#5
May1106, 07:25 PM

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By convention, if we use a lowercase letter to denote a function, we use an uppercase letter to denote its antiderivative.
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. 


#6
May1106, 08:51 PM

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according to some bumper stickers i have seen, it stands for the president.



#7
May2606, 06:22 AM

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With "_ _ _" after it?



#8
May2606, 11:34 PM

P: 555

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? 


#9
May3006, 11:18 PM

P: 258

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.



#10
May3106, 06:51 AM

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#11
May3106, 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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