Question

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

Answer 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.

Answer 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.