1. Nov 26, 2011 #1

   MozAngeles

   

   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 M_x and M_y the integration are impossible.

    

   MozAngeles, Nov 26, 2011
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3. Nov 30, 2011 #2

   susskind_leon

   

   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.

    

   susskind_leon, Nov 30, 2011

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