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Math Help - Find the area surrounding the curves

  1. #1
    Newbie
    Joined
    Sep 2007
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    10

    Find the area surrounding the curves

    Like the header says.

    a) y = x, y = 1/sqrt(x), x = 2

    b) sqrt(x) + sqrt(y) = 1, x = 0, y = 0

    Have been dwelling over this for some time, so I figured.. Why not just try to get some help Please
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    1,631
    You mean, the area surrounded by the 3 curves. Not surrounding the curves.

    a) y1 = x, y2 = 1/sqrt(x), x = 2

    Sketching the graphs of those 3, the easiest area is by making the
    dA = (y1 -y2)dx
    The integration, or the boundaries of dx, then is from x=1 to x=2.
    x=1 being at the intersection of curves y1 and y2.
    So,
    A = INT.(1-->2)[x - 1/sqrt(x)]dx
    A = INT.(1-->2)[x -x^(-1/2)]dx.
    A = [(1/2)x^2 +2sqrt(x)]|(1-->2)
    A = [(1/2)(2^2) +2sqrt(2) -0 -0]
    A = 2 +2sqrt(2) = 2(1 +sqrt(2)) = 4.82843 sq.units --------answer.

    --------------------------------

    b) sqrt(x) + sqrt(y) = 1, x = 0, y = 0

    I don't know how to graph the "sqrt(x) + sqrt(y) = 1" now.

    If you know how to use a graphing calculator, see how goes the graph of that. Then it should be easy to choose your dA.
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