Area bounded by Curves Integration Question

[rkltkdlee]

Homework Statement

Find the region bounded by the two functions from y=0 to y=2

equations given:
x=(y-1)2 -1
x=(y-1)2 +1

express x as a function of y and integrate it with respect to y

Homework Equations

equations given:
x=(y-1)2 -1
x=(y-1)2 +1

The Attempt at a Solution

Set x as a function of y

sqrt(x+1) + 1 =y
sqrt(x-1 ) + 1 = y

4. The confusion

The second equation doesn't actually exist until x =1...does that mean I have to just integrate from 1 to 2? But...

It says from y=0 to y=2... I am confused about this. I am told to express x as a function of y and integrate it with respect to y... I am unclear as to the meaning of this. It would make more sense if this was x=0 to x=2... please help!

 

[Vorde]

Okay, I think the two equations you have are:
$x=(y-1)^2-1$
$x=(y-1)^2+1$

Think about the wording: "express x as a function of y", this means that you aren't supposed to change the equations because x should be isolated, and it already is. Remember now that when you are integrating a function $x=f(y)$ that the bounds of integration will be from $y=a$ to $y=b$, not X's.

So you don't have the manipulate the equations because x is already isolated, can you see where to go on from here?

 

[rkltkdlee]

Ahhh yes! Thank you! The wording confused me greatly; I think that was the problem. Thank you for your time.