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Homework Help: Area of a tunnel with two functions creating the cross section

  1. Apr 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Two curves/functions make up one side of a tunnel (the tunnel is symmetrical, so the other side is the same)
    Function 1: y = 5 + (2/((x-4)^3))
    Function 2: y = (x -1)^3 - 5
    I need to find the area of the tunnel, so I can find the amount of dirt that needs to be removed,
    So I need the area of one side of the tunnel cross section.

    This is what it looks like with both functions. Where they meet at X = 3 and Y = 3, is where they join.
    http://img203.imageshack.us/img203/9497/04142013image003.jpg [Broken]

    So The top of the tunnel is Function 1, when F1 meets Function 2, function 2 becomes the side of the tunnel. The tunnel cross section looks like this:
    http://img703.imageshack.us/img703/8360/tunnela.png [Broken]
    Remembering this is just the right side of the tunnel, the left side is the same, flipped over the Y axis, to form a full tunnel.

    2. Relevant equations

    I thought it would just be an integral with limits, but the more I thought about it, the less I believed that was correct. I don't really know what equation to use to find the area when the curves only intercept once not twice.

    Thanks for all your help!!!
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Apr 13, 2013 #2


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    Science Advisor
    Homework Helper

    You just want to integrate the difference between f11 and 0 until the point where f12 becomes greater than 0, then integrate the difference between f11 and f12 until they intersect, don't you? Just split it into two integrals.
    Last edited by a moderator: May 6, 2017
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