(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the tripple integral [tex]\int\int\int_D(x^2-z)dV[/tex] in the doman D which is bounded by the cube [tex]-1\leq{x}, y, z\leq{1}[/tex] and lies below the parabloid [tex]z=1-x^2-y^2[/tex].

Okay, so we have not yet learned these in class, however, we were wanted to try this using intuition from double integrals. Can someone tell me if my "intuition" is wrong?

Thanks.

3. The attempt at a solution

[tex]\int\int\int_D(x^2-z)dV=\int\int\int_D(2x^2+y^2-1)dV=2\int_{-1}^1x^2dx\int_{-1}^1dy\int_{-1}^{1}dz+\int_{-1}^1dx\int_{-1}^1y^2dy\int_{-1}^1dz-\int_{-1}^1dx\int_{-1}^1dy\int_{-1}^1dz[/tex]

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# Tripple integral

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