anonymous
  • anonymous
Find the volume of the region between the graph of f(xy)=36−x^2−y^2 and the xy plane. I'm not too sure how to set up the double integral-- but 36-x^2-y^2 is what we will integrate? right??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
the x will surely go from 0 till 6
anonymous
  • anonymous
or maybe from -6 to 6
anonymous
  • anonymous
ok I guess I have an idea

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anonymous
  • anonymous
the level surface of this is always a circle
anonymous
  • anonymous
when we look at the xy plane it is a circle with center (0,0) and radius 6
anonymous
  • anonymous
so x goes from -6 to 6 and y goes from
anonymous
  • anonymous
would we then use x^2 + y^2 = r^2 to solve for y?
anonymous
  • anonymous
\[-\sqrt{36-x ^{2}}\] to \[\sqrt{36-x ^{2}}\]
anonymous
  • anonymous
hmm this cannot be good... damn it would mean that the integral is 0
anonymous
  • anonymous
I'm going to think about it over dinner-- will be back in 20 min
anonymous
  • anonymous
ok, I am going to bed soon

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