Find the area of the following two curves.
y= sqrt(x)
y= x-2
Since x ≥ 0 for y = √x
the graph shows that we cannot have a closed region.
see ...
http://www.wolframalpha.com/input/?i=plot+y%3D+√%28x%29+%2C+y%3D+x-2
Exactly what does that mean? Im a little confused.so what will be the answer?
Thanks
Take a look at
http://www.jiskha.com/display.cgi?id=1398307458
where I discussed this problem.
To find the area between two curves, we need to determine the points of intersection and then integrate the difference between the two functions over that interval.
First, we set the two equations equal to each other to find the points of intersection:
sqrt(x) = x - 2
To solve this equation, we need to square both sides to eliminate the square root:
(x - 2)^2 = x
Expanding the left side of the equation:
x^2 - 4x + 4 = x
Rearranging the terms:
x^2 - 5x + 4 = 0
Now we can factor this equation:
(x - 1)(x - 4) = 0
Setting each factor equal to zero:
x - 1 = 0 or x - 4 = 0
x = 1 or x = 4
So, the two curves intersect at x = 1 and x = 4.
Next, we need to determine the interval over which we will integrate. Since the curve y = sqrt(x) is above the curve y = x - 2 between x = 1 and x = 4, the integral will be:
∫[1, 4] [(sqrt(x) - (x - 2))] dx
Integrating this expression will give us the area between the two curves.