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April 10th, 2017, 05:19 PM  #1 
Senior Member Joined: Jan 2017 From: Toronto Posts: 163 Thanks: 2  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. 
April 11th, 2017, 04:32 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,919 Thanks: 785 
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 xyplane is also a boundary?

April 11th, 2017, 10:38 AM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 1,692 Thanks: 860  
April 12th, 2017, 06:25 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,919 Thanks: 785 
I wouldn't. Hopefully, Zollen will get back to us to tell us what the problem really says!

April 12th, 2017, 03:41 PM  #5 
Senior Member Joined: Jan 2017 From: Toronto Posts: 163 Thanks: 2 
Yes. z must be positive.

April 13th, 2017, 03:36 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,919 Thanks: 785 
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 Last edited by Country Boy; April 13th, 2017 at 03:39 AM. 

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double, equation, equestion, general, integration 
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