What does the big F stand for?

  1. 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. jcsd
  3. 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 :smile:
     
    Last edited: May 10, 2006
  4. HallsofIvy

    HallsofIvy 40,241
    Staff Emeritus
    Science Advisor

    "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]?
     
  5. SO a capital F means the antiderivative of a function?
     
  6. Hurkyl

    Hurkyl 16,090
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
     
  7. mathwonk

    mathwonk 9,673
    Science Advisor
    Homework Helper

    according to some bumper stickers i have seen, it stands for the president.
     
    Last edited: May 11, 2006
  8. HallsofIvy

    HallsofIvy 40,241
    Staff Emeritus
    Science Advisor

    With "_ _ _" after it?
     
  9. 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?
     
  10. 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.
     
  11. HallsofIvy

    HallsofIvy 40,241
    Staff Emeritus
    Science Advisor

    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!
     
  12. arildno

    arildno 12,015
    Science Advisor
    Homework Helper
    Gold Member

    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]
     
    Last edited: Jun 1, 2006
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook