Off-center vortex

If we have a off-center vortex with strength $n$ in a superfluid contained in a cylindrical container (with distance $r$ away from center), the angular momentum is determined from the following integral: $$\int r dr d\theta dz \rho r v(r)$$ Now suppose the shortest distance from the vortex to the edge of the container is $r_e$, and we ignore the variation of density $\rho$ in the core, how should the integral be evaluated? Is it correct to just take the position of the vortex as the new center and integrate all the way up to $r_e$ or that vortex still have influence for regions outside the circle with radius $r_e$?

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 Hi user12916, and welcome to Physics Stack Exchange! I notice that you've tagged this homework, so I do want to ask: which part of this is the actual homework (or homework-like) problem you were given, and what is the part of it that you're asking about? – David Zaslavsky♦ Oct 9 '12 at 23:22