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Surface integral problem.

  1. Dec 6, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider the surface S formed by rotating the graph of y = f(x) around the x-axis between x = a and x = b. Assume that f(x) ≥ 0 for axb. Show that the surface area of S is 2π times integral of f(x)sqrt(1 + f ' (x)^2) dx from a to b.

    http://i.imgur.com/qFeGP.png

    2. Relevant equations

    The integral of the magnitude of the cross product of the partial derivatives of parameterization vector, r = r(s,t). The region is R.

    3. The attempt at a solution

    I tried parameterizing the surface with parameters of x and f(x). The surface I set as g(x,f(x)). But when I took the cross product of that thing, I ended up with a useless statement involving partial derivatives which does not lead to the solution.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Dec 6, 2012
  2. jcsd
  3. Dec 7, 2012 #2

    haruspex

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    That's not an equation. Can you elaborate?
    Please post details of you working.
     
  4. Dec 7, 2012 #3

    tiny-tim

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    hi countzander! :smile:
    why so complicated? :cry:

    just use trig! :smile:

    (and f' = tan)
     
  5. Dec 7, 2012 #4
    http://i52.photobucket.com/albums/g12/countzander/Untitled-1.png [Broken]
     
    Last edited by a moderator: May 6, 2017
  6. Dec 7, 2012 #5

    LCKurtz

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    That isn't two parameters. ##x## is free to use as a parameter but then ##f(x)## is determined. You need another parameter if you want to do it that way. I would suggest ##\theta##, the angle of rotation as the second parameter. Express your surface as$$
    \vec R(x,\theta) = \langle x, ?, ?\rangle$$where the question marks are the appropriate expressions for ##y## and ##z## in terms of ##x,\, f(x),\, \theta##.
     
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