Math (6)

Find the area of the following two curves.
y= sqrt(x)
y= x-2

Note: People have been telling me that the two lines do not intersect but they do there has to be an answer. please help me.
Thanks

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asked by Mia
  1. The lines do intersect.
    sqrt(x) = x-2
    x =(x-2)^2 =x^2-4x + 4
    x^2-5x+4=0
    (x-1)(x-4)=0
    x=1,4 but 1 does not work if you plug in x=1 to both equations, so the only answer is x=4.

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    posted by JIm
  2. Jim, they do intersect at one point only, thus creating an open region on the left.
    By squaring you are introducing a part of the graph which was originally undefined.

    y = √x is defined only for x ≥ 0

    Mia:
    Both Steve and I gave answers to this earlier
    http://www.jiskha.com/display.cgi?id=1398476046

    Are you finding the area between the two curves from the y-axis to the point (4,2) ?

    That looks straightforward and should pose no problems for you.
    However, you did not say that.

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    posted by Reiny

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