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Homework Help: Double Integral Volume Problem

  1. Nov 13, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid enclosed by the cylinders z=x^2, y=x^2, and the planes z=0 and y=4.

    2. Relevant equations

    3. The attempt at a solution

    ∫∫ x^2 dA

    For the limits of integration, I obtained y=x^2 and y=4, x=0 and x=2

    I changed the order of integration and obtained x=y^(1/2) and x=0, y=0 and y=4.

    ∫0 to 4 ∫0 to y^(1/2) x^2 dxdy

    (1/3) * ∫0 to 4 (y^(3/2)) dy


    = 64/15

    I am not sure where I am going wrong. The back of the book says it's 128/15 though. In fact, for a few problems I've got (1/2)*the correct answer for these problems.
  2. jcsd
  3. Nov 13, 2008 #2


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    Science Advisor
    Homework Helper

    You are only doing the volume in the first quadrant (where x>0). x should run from -sqrt(y) to +sqrt(y).
  4. Nov 13, 2008 #3
    I had a feeling that's what was going wrong. Thank you.
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