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Evaluate the integral $$ \iiint \limits_D z \ dV ,$$ where $D$ is the region bounded by the planes $y = 0$, $x = 0$, $z = 0$, $z = 1$, and the cylinder $x^2+y^2=1$ with $x,y \ge 0$.

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    Is this homework? Could you explain what the problem is? Where did you get stuck?2011-10-25
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    Can you rephrase the question, so it sounds like a question and not an order?2011-10-25
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    @J.M.: I’ll not change it back, but I much prefer $dV$ to $\mathrm dV$.2011-10-25
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    @Brian: Knuth's argument for a Roman-type d is still ringing in my brain. If you've got a nice argument for not doing so for multiple integrals, I'll gladly undo.2011-10-25
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    @J.M.: Purely a matter of taste: I think that it looks much better, and I don’t consider the $d$ an operator.2011-10-25
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    Surely this would be easier in cylindrical coordinates?2011-10-25

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