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Centroid position of Lamina

  1. May 11, 2015 #1
    1. The problem statement, all variables and given/known data

    A lamina is bounded by the x-axis, the y-axis, and the curve ##y = 4 -x^2.## Determine the centroid position ##(\bar{x},\bar{y})## of the lamina.

    2. Relevant equations

    ## A = \int_a^b (f(x) - g(x)) dx ## (Area)

    ##\bar{x} = \frac{1}{A}\int_a^b x(f(x) - g(x)) dx ##

    ##\bar{y} = \frac{1}{A}\int_a^b \frac{1}{2}(f(x)^2 - g(x)^2) dx ##

    3. The attempt at a solution

    I made a sketch and determined ## a = 0## and ##b = 2 ## for the limits.

    Then just plugged into the above equations.

    With this I determined the area to be ##A=16/3##

    ##\bar{x} = \frac{3}{4} ##

    ##\bar{y} = \frac{8}{5}##

    Therefore centroid position is ##(\frac{3}{4},\frac{8}{5})##

    Could someone kindly verify this?
     
  2. jcsd
  3. May 11, 2015 #2

    Zondrina

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    Homework Helper

    Everything looks good at a glance.
     
  4. May 13, 2015 #3
    It is correct, thank you :smile:. I used an online calculator to verify it. I'll write out a solution for any future viewers.
     
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