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Please help, i cant do this center of mass problem

  1. Feb 22, 2006 #1
    [​IMG]

    it gave me two figures and explained how they look, so i sketched them as they are. i dont have a problem with centroids, but i do with this particular problem.

    this is the question:

    Let R be the region that lies between the curves of y=X^m and y=x^n.
    0=<x=<1
    (0 is less than or equal to x, which is less tahn or euqal to 1)

    0=<n<m
    a) sketch the graph (already done)
    b) find the coordinates of the centroid of R
    :confused:

    please help, i dont even know how i can get the area of these two figures
     
  2. jcsd
  3. Feb 22, 2006 #2
    also what would R be? would it be x^n-x^m
     
  4. Feb 22, 2006 #3

    quasar987

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    Have you ever heard something to the avail of "[itex]\int_a^b f(x)dx[/itex] is the area under the curve f(x) from a to b"?
     
  5. Feb 22, 2006 #4
    youre right, but where would the object be?
     
  6. Feb 22, 2006 #5
    would the object take form in the shaded region?
     
  7. Feb 22, 2006 #6

    HallsofIvy

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    There is no shaded region! Also it makes no sense to say "Would R be x^n-x^m?" because R is a region not a function. Okay, you have drawn the graphs. You are looking for the centriod of the region between the two graphs and between x= 0 and x= 1. Integrate xm- xn (assuming m> n) between 0 and 1.
     
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