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Triple integral to find the volume

  1. Apr 19, 2010 #1
    1. The problem statement, all variables and given/known data

    use a triple integral to find the volume of the region that is common to the interiors of z^2 +y^2 + z^2 = 1 and x^2 + z^2 = 1

    2. Relevant equations

    Would I just calculate the are of the disc? I set up a triple integral as inte [0 to 1] 2nd inte [0 to sqrt(1-z^2)] 3rd inte [0 to 0] dy dx dz
    That doesnt really work though since after the first integration it would just be 0 (??)
    How would you set up this triple integral? (I might just not be understanding what the region is??)
  2. jcsd
  3. Apr 20, 2010 #2


    Staff: Mentor

    This isn't a double integral, so the region of integration isn't a disk or other two-dimensional object. The region of integration is the three-dimensional space that is "common to the interiors of z^2 +y^2 + z^2 = 1 and x^2 + z^2 = 1."
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