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I don't know if this should actually be asked on the English stackexchange. It seemed like I would find better answers here.

I have all but finished an undergraduate degree in mathematics in the United States, but I have never once heard the term "primitive" to mean "antiderivative" until recently, when someone from Europe pointed it out to me. According to him, it's a common term there. So I was wondering if people could give me an idea of how common this term is, and where. I know for sure that if someone says "primitive" to a math student in the US, that the student won't know what he is talking about. Does the reverse hold for "antiderivative" (or the also common "integral") elsewhere?

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Apostol's "Calculus" volume 1 uses "primitive" in that sense 41 times, whereas "antiderivitive" is only used 4 times. Two of those are in the main text, always as part of an "or antiderivative" after the term "primitive", and the other two are in the index.

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    Upvoted for cunning use of ctrl-F.2011-06-26
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In complex analysis the antiderivative is often refered to as the primitive.

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    I've since taken two semesters of complex analysis and my professor never used the term (anti-derivatives aren't even that important in the field anyway).2012-06-17
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I think this is due to Richard Courant. In his 2 volume book Differential and Integral Calculus, he uses the term 'primitive' to mean antiderivative.

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    It's certainly a lot older than Courant. See http://jeff560.tripod.com/mathword.html which traces "primitive" back to Lagrange in 1797. For "anti-derivative" the first reference they have is 1903.2011-06-26
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I can just say that "the primitive function" (primitivní funkce) is the only official name of this object in Czech. Also, I think that the most standard English term is not "antiderivative" but rather "indefinite integral".

http://en.wikipedia.org/wiki/Antiderivative

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    Though I don't think it's exactly standard, I like the use (saw this in Apostol, I think?) of "indefinite integral" to specifically mean $F(x)=\int_a^x f(t)dt$ for some f and a. Of course this turns out to be the antiderivative when f is continuous, but...2011-06-26
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In the Dutch language, the antiderivative is known as the "primitieve".

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    @kahen: (Almost) the same in German: Stamm$f$unktion2011-06-26