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I don't understand in what circumstance something could vanish when doing the complex integration. Vanish this word sounds too abstract to me.

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closed as not a real question by Pedro Tamaroff, Dylan Moreland, Chris Eagle, lhf, Davide Giraudo Apr 27 '12 at 18:26

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1 Answer

Vanish means "goes away", "is zero" or any other similar expression that conveys the fact the term acts as the additive identity $0$.

I don't understand why you complain about abstractness. It is just an expression. For example, for any $f(x)$ such that $f(x)=-f(-x)$, the integral

$$\int_{-a}^a f(x) dx$$ vanishes, i.e.

$$\int_{-a}^a f(x) dx=0$$

There is no more mystery than that.

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English is not my first language –  Megan Apr 27 '12 at 18:20
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@Megan Neither is it mine. But in general, you can just look the word up in a dictionary. In this case, I simply find 2. Mathematics To become zero. Used of a function or variable. –  Pedro Tamaroff Apr 27 '12 at 18:22
    
To be fair, a lot of the online dictionaries don't seem to have that definition. The OED does, because it's great, but I don't think that's free. –  Dylan Moreland Apr 27 '12 at 18:39
    
@Dylan It is totally free! See the link! www.thefreedictionary.com/vanish –  Pedro Tamaroff Apr 27 '12 at 20:11
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