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Math Help - Areas Between Curves

  1. #1
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    Areas Between Curves

    Find the area enclosed by the 3 lines:

    y = 1/x, y = x, and y = x/4 where x > 0

    The answer is supposed to be LN 2

    I know that one of the first steps is to solve the equations simultaneously, but I'm not sure how to so what when you're working with 3 equations. Anyway, this is how I did it.

    1/x = x

    1/x -x = x/4

    1/x - x - x/4 = 0

    x = +/- 2/sqrt(5)

    So I integratd between +/- 2/sqrt(5) and I did not get LN 2.

    Can someone help me with this, please?
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  2. #2
    Junior Member
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    You have 2 lines, y=x, and y=x/4, and a curve y=1/x.
    You can not fin only one intersection point.
    You have to find the intersection point using 2 equations at a time.
    The two line, a line and the curve, the other line and the curve.
    Try to plot the graph to realy see your area.
    After that try to integrate.
    Hope this helps!
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  3. #3
    Junior Member
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    ok
    here you go,
    y=x and y=1/x
    x=1/x, so x^2=1, since x>0, x=1 is the intersection point.

    y=x and y=x/4
    x=x/4
    4x=x
    3x=0
    x=0

    y=1/x, y=x/4
    1/x=x/4
    x^2=4, since x>0, x=2

    Graph the functions:
    Attached Thumbnails Attached Thumbnails Areas Between Curves-3.jpg  
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