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April 10th, 2017, 04:19 PM   #1
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Double Integration about general equation

Find the volume bounded by z = x^2 + y^2 and z = y.

Answer: pi/32

Any tips would be much appreciated.
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April 11th, 2017, 03:32 AM   #2
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There is no area bounded by these. The first is a cylinder, the second is a plane cutting the cylinder. You need another plane to bound a finite region. Was there a condition that z be positive? That is, that the xy-plane is also a boundary?
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April 11th, 2017, 09:38 AM   #3
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Quote:
Originally Posted by Country Boy View Post
That is, that the xy-plane is also a boundary?
that's what I would assume
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April 12th, 2017, 05:25 AM   #4
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I wouldn't. Hopefully, Zollen will get back to us to tell us what the problem really says!
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April 12th, 2017, 02:41 PM   #5
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Yes. z must be positive.
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April 13th, 2017, 02:36 AM   #6
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Apparently I did not look closely enough at the original problem! is a paraboloid, not a cylinder, and together with z= y does define a finite region.

Taking z= y, the intersection of the plane and the paraboloid satisfies or . Complete the square in y by adding 1/4 to both sides: . That projects to the circle in the xy plane with center at (0, 1/2) and radius 1/2. We can cover that by taking x from -1/2 to 1/2 and, for each x, taking y from to .

The volume is given by
Thanks from topsquark and zollen

Last edited by Country Boy; April 13th, 2017 at 02:39 AM.
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