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Area bounded by Curves Integration Question

  1. Nov 24, 2012 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations

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


    3. 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!
     
  2. jcsd
  3. Nov 24, 2012 #2
    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?
     
  4. Nov 24, 2012 #3
    Ahhh yes! Thank you! The wording confused me greatly; I think that was the problem. Thank you for your time.
     
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