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Math Help - A complicated equal area problem

  1. #1
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    A complicated equal area problem

    Let R be the region bounded by the parabola y=x-x^2 and the x axis from 0 to 1

    find the equation y=mx that divides this region into two regions of equal area
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  2. #2
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    Quote Originally Posted by whocares27 View Post
    Let R be the region bounded by the parabola y=x-x^2 and the x axis from 0 to 1

    find the equation y=mx that divides this region into two regions of equal area
    Please see attached graph, and then try to understand and solve.
    Attached Thumbnails Attached Thumbnails A complicated equal area problem-graph15.jpg  
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  3. #3
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    i understand what you showed me with x=.5 would bisect it in half, but i need a line that fits the equation y=mx meaning it will have to go through the origin
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  4. #4
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    We want that
    Yellow = Green + Red

    For a given h, we can calculate the green triangle's area.
    By integration from 0 to h, we can get the sum of Yellow and Green.
    By integration from h to 1, we find Red.

    Using our equation above (Yellow = Green + Red) and these methods for calculating the areas, we can find h.
    then m in y=mx can be calculated quickly:

    m=(h-h^2)/h=1-h, which is
    m= 1 - (cubic root of half)
    Attached Thumbnails Attached Thumbnails A complicated equal area problem-parabo.gif  
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  5. #5
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    thank you very much
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  6. #6
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    Hello Gorilla,

    Which software do you use to draw graphs??? Where can I get that software???
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  7. #7
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    Hi Shyam!
    WZgrapher:

    WZGrapher Function Grapher
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