compute volume of a figure bounded by $z=2-\sqrt{x^2+y^2}$ and $z=0$. I don't know how to do this, thanks for help!
2026-03-29 12:38:36.1774787916
question on multiple integrals, volume
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The "boundary" curve is defined by: $2-\sqrt{x^2+y^2} = 0$, or $x^2+y^2 = 4=2^2$ which is a circle centered at $(0,0)$, and having radius $r = 2$. Cylindrical coordinates seems to be the natural choice here. So:
$V = \displaystyle \int_{0}^{2\pi} \int_{0}^2 \int_{0}^{2-r} rdzdrd\theta$