Assuming [tex]E=\{(x,y,z)~:~\sqrt{x^2+y^2}<z<1\}[/tex], so that the region is essentially a cone with base radius 1 and height 1, the triple integral of [tex]f(x,y,z)[/tex] can be expressed as
[tex]\displaystyle\iiint_Ef(x,y,z)\,\mathrm dV=\int_{x=-1}^{x=1}\int_{y=-\sqrt{1-x^2}}^{y=\sqrt{1-x^2}}\int_{z=\sqrt{x^2+y^2}}^{z=1}f(x,y,z)\,\mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
or
[tex]\displaystyle\iiint_Ef(x,y,z)\,\mathrm dV=\int_{y=-1}^{y=1}\int_{x=-\sqrt{1-y^2}}^{x=\sqrt{1-y^2}}\int_{z=\sqrt{x^2+y^2}}^{z=1}f(x,y,z)\,\mathrm dz\,\mathrm dx\,\mathrm dy[/tex]
