When we took the integral of a function f, the result is: [tex]\int f(x)dx = F(x) + C[/tex] But, F(x) + C can be rewritten like: [tex]F(x) + C = \mathcal{F}(x)[/tex] So, my first ask is: which is the name given for ##F(x)## and for ##\mathcal{F}(x)## ? I can't call both of primitive of f, because it's confuse. I already heard the term "family of antiderivative", I think that this term is the name of ##\mathcal{F}(x)##, thus, maybe, primitive is better for ##F(x)##. What do you think?(adsbygoogle = window.adsbygoogle || []).push({});

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Second question: by FTC: [tex]\int_{x_0}^{x}f(x)dx = F(x) - F(x_0)[/tex] implies that: [tex]F(x) = \int_{x_0}^{x}f(x)dx + F(x_0)[/tex] This result, F(x), represents the ##F(x)## or the ##\mathcal{F}(x)## of the my 1st question?

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OBS: if you affirm that F(x) of the 2nd question is equal to ##\mathcal{F}(x)## this implies that ##\int_{x_0}^{x}f(x)dx = F(x)## and ##F(x_0)=C## .

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# Math Primitives

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