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Finding coordinates of a centroid

  1. Feb 27, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the exact coordinates of the centroid for the region bounded by the curves x=5-y^ 2 and x=0

    I am not sure about this one because it uses dy instead of dx i think.

    I tried to set it up like this

    x= [0.5∫(5-y^2)^2 dy from -5 to 5]/[ ∫(5-y^2)dy from y=-5 to 5]

    This does not give me the right answer, can anyone help? I have no trouble solving it if it gives me a region bounded by y=x (for example), but i think that the centre of mass in y-variable means that Mx and My are reversed?

    Very confused, thanks for any help you can give
    2. Relevant equations

    x=My/A
    y=Mx/A


    3. The attempt at a solution
     
  2. jcsd
  3. Feb 27, 2013 #2

    haruspex

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    Why the 0.5 at the front?
    Also, you have the wrong range for y.
     
  4. Feb 27, 2013 #3
    i added the 0.5 because i tried using the My equation for centre of mass in y-variable whch is density/2∫[f(y)^2-g(y)^2]dy from a to b. Would the range be -5^.5 to 5^.5?
     
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