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Can the volume Integral of a non zero function be zero? e.g if i evaluate the triple integral of: $$ xy^2 +2yz^2 $$ bounded by $$-1<x,y,z < 1$$ I get zero when I evauluate this.

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  • $\begingroup$ Why do you think it can't? $\endgroup$
    – user856
    Oct 27, 2018 at 13:26
  • $\begingroup$ Indeed, the terms $xy^2$ and $2yz^2$ both have integral zero on your cube. $\endgroup$
    – GEdgar
    Oct 27, 2018 at 14:27

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Yes.It can be zero.Suppose you are evaluating double integral over some area and the part of graph above and below $xy$ plane is same,then u will get zero there. Similar case occurs in volume integral.

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