## What does the big F stand for?

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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 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
 Recognitions: Gold Member Science Advisor Staff Emeritus "f(x)-sinb=F(a)-F(b)" makes no sense. Are you sure it wasn't something like $\int_b^a f(x)dx= F(a)- F(b)$?

## What does the big F stand for?

SO a capital F means the antiderivative of a function?
 Recognitions: Gold Member Science Advisor Staff Emeritus 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.
 Recognitions: Homework Help Science Advisor according to some bumper stickers i have seen, it stands for the president.
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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?
 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.

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 Recognitions: Gold Member Homework Help Science Advisor Actually, I hereby declare that the following definition of F(x) is unique and unviolable: $$F(x)=\frac{\pi}{1+\frac{\pi}{1+\frac{x}{e+\pi}}}$$