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We have to consider the integral of $$\int_{0}^{1}\int_{0}^{1-x^2} \int_{0}^{1-x}f(x,y,z)dzdydx$$

First we're told to graph the region of integration, so I started that but I'm not exactly sure what I'm doing. I end up with something that looks like a slim triangular slice of a cone, but I don't know if it's correct. Is it?

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    $\begingroup$ Formatting help: try $\int_{lower}^{upper}f(x)dx$. $\endgroup$
    – Théophile
    Dec 4, 2017 at 3:05
  • $\begingroup$ the integral doesn't represent a surface. Assuming $f$ has units of density, then the integral represents the total amount of "stuff" in a volume. $\endgroup$
    – Sort of Damocles
    Dec 4, 2017 at 3:18

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