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Maximum of a triple integral

  1. Jan 15, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the region E for which the triple integral:

    (triple integral over E) (1 - x^2 -2y^2 -3z^2) dV is a maximum.

    2. Relevant equations



    3. The attempt at a solution

    I remember in earlier math courses finding the derivative of a single variable integral, does this problem involve finding the derivative of a triple integral and setting it equal to zero to find the maximum? If so, how would you do that?
     
  2. jcsd
  3. Jan 15, 2010 #2

    tiny-tim

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    Hi phrygian! :smile:

    You're making this too complicated …

    any region in which the integrand is positive will increase the integral, and any region in which the integrand is negative will decrease it …

    soooo … ? :wink:
     
  4. Jan 15, 2010 #3

    HallsofIvy

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    In other words, where is [itex]1 - x^2 -2y^2 -3z^2\ge 0[/itex]?
     
  5. Jan 15, 2010 #4
    So the region is when z = sqrt( (-2y^2 - x^2)/3 )? Is this a complete answer how do you describe the region?
     
  6. Jan 15, 2010 #5

    tiny-tim

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    Hi phrygian! :smile:

    (have a square-root: √ and try using the X2 tag just above the Reply box :wink:)
    erm :redface: … you can't have √ of a negative nnumber, can you? :wink:

    Try again. :smile:
     
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