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Mass of solid and center of mass

  1. Apr 20, 2009 #1
    1. The problem statement, all variables and given/known data
    a solid in the first octant is bounded by the planes y=0 and z=0 and by the surfaces z=4-x^2 and x=y^2. its density function =kxy, k is a constant. find the mass of the solid and the center of mass



    2. Relevant equations
    My= double integral of D[x*kxy]dA
    Mx=double integral of D[y*kxy]dA
    M= double integral of D[kxy]dA
    xbar=My/M
    ybar=Mx/m

    3. The attempt at a solution
    this problem is way to complicated for me and I have a test on it this Thursday. Please guide me through the steps. What is the region D. What is dA. and do I even have the equations right or is the should I be using xbar=Myz/M, ybar=Mxz/M, and zbar=Mxy/M. Please explain how to solve these type problems. I need help!!
     
  2. jcsd
  3. Apr 21, 2009 #2

    Mark44

    Staff: Mentor

    D is not used correctly. I believe that it is supposed to represent the region over which integration is to be performed. D is the region in the first quadrant of the x-y plane that lies under the two paraboloids. You absolutely need a sketch of the solid you're working with, but as far as I can tell you haven't done this yet. You need to have a sketch of the solid in order to get the correct limits of integration in your iterated integral.

    dA is a rectangular bit of the region D whose dimensions are delta_x times delta_y.

    For your moment formulas, check your book. They should be listed there.
     
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