What Does the Big F Represent in Equations?

[Line]

What does the big F stand for in equations like

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

It's not like the little f in function.

 

[bomba923]

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]

"f(x)-sinb=F(a)-F(b)" makes no sense. Are you sure it wasn't something like $\int_b^a f(x)dx= F(a)- F(b)$?

 

[Line]

SO a capital F means the antiderivative of a function?

 

[Hurkyl]

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]

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

 

[HallsofIvy]

With "_ _ _" after it?

 

[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?

 

[Theelectricchild]

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]

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]

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