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how can I solve this problem I already have the final answer but I don't know how to solve it , the answer for this problem is $(V=8(pi-1/3)$ I tried solving it with this:

$\int_{-2}^2\int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}}\int_0^{x^2+y^2}dzdydx$

but it didn't work

Write an iterated triple integral in the order dzdydx for the volume of the region bounded below by the xy-plane and above by the paraboloid $z = x^2 + y^2$ and lying inside the cylinder $x^2 + y^2 = 4$?

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You should switch to cylindrical coordinates instead. Your integral will change to: $4 \int_0^2 \int_0^{\pi/2} \int_0^{\rho^2} \rho dz d\phi d\rho $

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  • $\begingroup$ But I need it in cartesian coordinates $\endgroup$ – TheNightKing Mar 21 '19 at 20:20
  • $\begingroup$ I suggest you to change the limits to those for quarter of a circle and then multiply by 4 It will give right answer $\endgroup$ – Tojrah Mar 22 '19 at 0:35

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