# Areas Between Curves

• May 10th 2007, 02:52 PM
zachb
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?
• May 10th 2007, 03:02 PM
alinailiescu
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!
• May 10th 2007, 03:21 PM
alinailiescu
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: