anonymous
  • anonymous
Find the volume of the region lying below z = 8 - x2 - y2 and above the xy-plane.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
it is calc 3! double integral i think!
KingGeorge
  • KingGeorge
First, you have to find where \(z=8-x^2-y^2\) intersects the plane \(z=0\). From there you can find the bounds with which to integrate.
anonymous
  • anonymous
i know that is the general scheme, but i cant set it up so if you can thatd be sweet bro

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KingGeorge
  • KingGeorge
Well, if \(z=0\), then \(x^2+y^2=8\). In other words, this is a circle of radius \(\sqrt{8}\) centered at the origin.
KingGeorge
  • KingGeorge
Thus, we might want to switch to polar coordinates. Have you worked with polar yet?
anonymous
  • anonymous
yes i was just about to say that, yes i have worked with them how would that look?
KingGeorge
  • KingGeorge
You would want to integrate r first, and then \(\theta\). Also, you know that \(x^2+y^2=r^2\) and \(\theta\) is the full rotation around. So the integral should look something like\[\int\limits_0^{2\pi} \int\limits_0^{\sqrt{8}} r(8-r^2) \quad dr \;\;d\theta\]
anonymous
  • anonymous
wow man great job! thanks alot!
KingGeorge
  • KingGeorge
You're welcome.

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