
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 10th, 2017, 04:19 PM  #1 
Senior Member Joined: Jan 2017 From: Toronto Posts: 120 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, 03:32 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,649 Thanks: 680 
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, 09:38 AM  #3 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,410 Thanks: 715  
April 12th, 2017, 05:25 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,649 Thanks: 680 
I wouldn't. Hopefully, Zollen will get back to us to tell us what the problem really says!

April 12th, 2017, 02:41 PM  #5 
Senior Member Joined: Jan 2017 From: Toronto Posts: 120 Thanks: 2 
Yes. z must be positive.

April 13th, 2017, 02:36 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,649 Thanks: 680 
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 02:39 AM. 

Tags 
double, equation, equestion, general, integration 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
General Integration Question  jmbeach1  Calculus  4  November 23rd, 2015 05:20 AM 
Solving a Double integral over a general region  Dan3500  Calculus  1  November 22nd, 2015 12:30 PM 
double integration  zell^  Calculus  6  April 16th, 2012 09:39 AM 
double integration help!!  skdnjswnd  Calculus  1  April 15th, 2009 07:20 PM 
Double integration (x/y)*e^y  Calculus  10  March 17th, 2009 04:28 PM 