Find the volume:
Under z =x^2+y^2 and above the region R={(x,y)| x^2+ y^2≤ 4}

Please explain step by step.

Question

Find the volume: 
Under  z =x^2+y^2 and above the region R={(x,y)| x^2+ y^2≤ 4}

Please explain step by step.

experimentx · Answer

the graph is going to be 3d-parabolic

we have to find the vertex first.

experimentx · Answer

attachment

experimentx · Answer

looks like 0,0,0 is going to be vertex

anonymous · Answer

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anonymous · Answer

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turingtest · Answer

ok, right off the bat I'm thinking cylindrical coordinates

turingtest · Answer

@Sillem  do you know how to convert this into cylindrical coordinates?

turingtest · Answer

If you convert this to cylindrical coordinates you will find that the region is bound by$$0\le\theta\le2\pi$$$$0\le r\le2$$and converting the equation we have for the parabaloid we get the bounds$$0\le z\le r^2$$remembering that $dV=rdrd\theta dz$ in cylindrical coordinates we now just have to integrate$$\int\int\int dV$$along the prescribed bounds, and in an order that makes some kind of sense.
I'll leave that final task to you.

turingtest · Answer

having a problem? 
please tell me where