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Homework Help: Triple integration for volume

  1. Nov 3, 2004 #1
    I have a group of problems that deals with the equations:

    f(x,y)= x^2+y^2
    g(x,y)=20-(x-4)^2-(y+2)^2

    Can someone help find the triple integral to find the volume.
     
  2. jcsd
  3. Nov 4, 2004 #2
    I would start off by making at the very least a rough sketch of the volume you are trying to find, that way you can find out the boundaries you are dealing with.
     
  4. Nov 4, 2004 #3

    HallsofIvy

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    Science Advisor

    It might help to clarify the problem: functions don't HAVE a volume!

    If you mean "find the volume of the region bounded by z= x2+ y2 (a paraboloid) and z= 20- (x-4)2- (y+2)2 (also a paraboloid)" then you need to determine where the two paraboloids intersect and "project" that down to the xy-plane.

    I get (x+2)2+ (y-1)2= 5, a circle. Subtract the two "z" values and integrate over that circle.

    (Please do not post the same question twice!)
     
    Last edited by a moderator: Nov 4, 2004
  5. Nov 4, 2004 #4
    Thanks for the help. I have problems with finding the intersection and projecting that on the x-y plane. We cannot use graphing calculators. Are there any easy ways to sketch the functions and/or find the intersection?
     
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