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What does the big F stand for?

  1. May 10, 2006 #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. May 10, 2006 #2
    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. May 11, 2006 #3


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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]?
  5. May 11, 2006 #4
    SO a capital F means the antiderivative of a function?
  6. May 11, 2006 #5


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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.
  7. May 11, 2006 #6


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    according to some bumper stickers i have seen, it stands for the president.
    Last edited: May 11, 2006
  8. May 26, 2006 #7


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    With "_ _ _" after it?
  9. May 26, 2006 #8
    I've seen this used as follows

    Other than that, doesn't ring a bell.

    EDIT: What math class did you see this in?
  10. May 30, 2006 #9
    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. May 31, 2006 #10


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    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. May 31, 2006 #11


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    Actually, I hereby declare that the following definition of F(x) is unique and unviolable:
    Last edited: Jun 1, 2006
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