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Homework Help: Mass using triple integrals

  1. Mar 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the mass m of the pyramid with base in the plane z = 9 and sides formed by the three planes y = 0 and y - x = 5 and 6x + y + z = 28, if the density of the solid is given by δ(x,y,z) = y.

    2. Relevant equations

    3. The attempt at a solution

    This problem is driving me insane. It takes me about 45 minutes of algebra to evaluate this incorrectly set up integral..

    I integrated y in the order dz dy dx, limits, respectively:

    9 to 28-6x-y
    0 to 5+x
    0 to 2

    Is that correct? I don't really know how to get the limits for x.. this is so hard to picture in my mind!

    To get 2, I solved the system 6x + y + z = 28 with z = 9 and y = 5 + x, and for 0, I just guessed.

    Help please!
  2. jcsd
  3. Mar 18, 2012 #2


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    Gold Member

    May I suggest that you draw a sketch and get a clear grip on the limits before you try to evaluate anything.
  4. Mar 18, 2012 #3
    Well, that's what I'm trying to do..
  5. Mar 18, 2012 #4
    I drew it again, the only thing different is that my order is dzdxdy.

    I don't understand how to picture these things, it's very difficult.. I just drew an xy plane noting that z = 9 for the base, and looked at that. What would you do?
  6. Mar 18, 2012 #5
    I think this is far beyond me.
  7. Mar 18, 2012 #6
    Nevermind, found a good explanation online of something called the "shadow method."
  8. Mar 18, 2012 #7


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    Gold Member

    Have you figured out it gets tricky if you use any order of integration other than dzdxdy?
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