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Calculating Triple Integrals in Mathematica

  1. May 3, 2013 #1
    1. The problem statement, all variables and given/known data

    Evaluate ∫∫∫[itex]\sqrt{x^{2} + y^{2}}[/itex] dA where R is the region bounded by the paraboloid y=x^2+z^2 and the plane y=4

    2. Relevant equations
    I believe this is a problem where cylindrical coordinates would be useful

    0 ≤ z ≤ [itex]\sqrt{4-x^2}[/itex]
    0 ≤ r ≤ 2 ( I think this is wrong).
    0 ≤ θ ≤ 2[itex]\pi[/itex]


    3. The attempt at a solution

    Integrate[ r^2, {\[Theta], 0, 2*Pi}, {r, 0, 2}, {z, 0, Sqrt[4 - r*Cos[\[Theta]]^2]}]

    There isn't an output when I enter this line. I checked for the syntax on the wolfram reference page so I think the problem is with the limits of integration.
     
  2. jcsd
  3. May 3, 2013 #2

    SteamKing

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    What is the source of your integral? What is it supposed to represent? I say this because you have a triple integral with dA rather than dV.
     
  4. May 4, 2013 #3
    This problem was given to me by my instructor.
     
  5. May 4, 2013 #4

    SteamKing

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    Yeah, I figured it wasn't revealed to you in a dream. But what is the ultimate source of this integral? Is it a problem out of a book? Have you solved faster than light travel? Is a new mathematics about to be revealed to us?

    You realize, I hope, that there seems to be something missing: You have a triple integral of a function with respect to what appears to be a differential element of area dA. Three integrations, two variables with respect to which the integration could be carried out. It's not clear how this integral is supposed to be calculated.
     
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