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No. It's a "Grothendieck construction", which uses the integral symbol as well. Specifically, it's the Grothendieck construction applied to a pseudopresheaf of discrete categories (i.e. sets) (which are the same things as presheaves of sets, since there are no coherence data to speak of).
Also, this is not the correct place to ask this question. Probably a good place to ask something like this is on math.se.
I suspect such a question would get closed, mostly because the answer is (I believe) "no": the category of elements is not a coend in any useful way. As Harry surmises, you may have been misled by the fact that some people use the integral sign to denote a category of elements, and the integral sign is also used for ends and coends.
There's some sense in which a category of elements is an end. It's a lax limit. But that seems some distance from what you're asking. So, if I were you, I wouldn't ask the question you describe.
Spice, if you can recognize a tensor product of modules as a coend, and if you can recognize geometric realization of a simplicial set as an coend, then you are probably well on your way to understanding coends. The nLab might help. Possibly you might find Mac Lane's "Milgram bar construction as a tensor product of functors" helpful and illuminating.
Recently there has been discussion on how effective math.stackexchange.com would be in answering queries at this level. The reports have not been so good.
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