What does it mean for an integral to "vanish"?

Question

I had a question;

What does it mean for an integral to vanish in complex analysis?

There is supposedly something, which says if the integral "vanishes," the sum of the residues is 0.

But what does it mean for the integral to "vanish," does it mean to diverge? To equal $0$?

Help is appreciated!

score 3 · Answer 1 · answered Nov 11 '14 at 16:42

3

Vanish Mathematics. (of a number, quantity, or function) to become zero.

answered Nov 11 '14 at 16:42

Pedro

can you advise me then: http://math.stackexchange.com/questions/959701/evaluate-int1-0-log21-x-log2x-dx/960157?noredirect=1#comment2074528_960157 please take a look at M.N.C.E's method. It says the integral $f(z)$ vanishes. But how can I check it evaluates to $0$? M.N.C.E. doesnt state the lower and upper limit, how can I check? From $-\infty \to +\infty$ the integral DIVERGES. Help? – Amad27 Nov 11 '14 at 16:52
@Amad27 You should ask MNCE. – Pedro Nov 11 '14 at 23:54
I did. but I didnt get a reply back. – Amad27 Nov 12 '14 at 08:32

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