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Center of mass

  1. Nov 26, 2011 #1
    1. The problem statement, all variables and given/known data
    Find teh center of mass of a thin infinite refion in the first quadrant bounded by the coordinate axes and the curve y=e-2x, if ρ(density)= xy


    2. Relevant equations



    3. The attempt at a solution
    I set M= ∫∫ xy dydx where y goes from 0 to y=e-2x, and x goes from 0 to infinity. I solved this and got 1/8

    but when i try to calculate Mx and My the integration are impossible.
     
  2. jcsd
  3. Nov 30, 2011 #2
    You're doing the integral wrong, mate! What have you got so far?
    I get [tex] \int_0^{e^{-2x}} y dy = \left[y^2/2\right]_0^{e^{-2x}} = e^{-4x}/2[/tex]
    [tex] M = \int_0^\infty dx \int_0^{e^{-2x}} dy xy = \int_0^\infty dx x \int_0^{e^{-2x}} dy y = \int_0^\infty x e^{-4x}/2 = 1 / 32[/tex]
    Now put one additional x or y, respectively into your integrand and do the calculation for Mx and My.
     
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