1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Surface area of smooth parametric surface

  1. Feb 11, 2010 #1
    Sorry I am new to the forum, I don't know how to type in the integrals and stuff.

    1. The problem statement, all variables and given/known data
    Let S be the portion of the surface y = x2 where 0 <= z <= X <= 2. Compute the surface area of S.

    2. Relevant equations
    r(u,v) = x(u,v)i + y(u,v)j + z(u,v)k
    A(S) = integral ru X rv dA


    3. The attempt at a solution
    My first attempt I did: x = ucosv, y = u2cos2v, and z = ucosv where 0<= u <= 2 and 0 <= v <= 2pi
    when I was doing ru X rv, got a lot of sines and cosines but everything canceled out at the end and became 0.

    Then I just decided to use x = x, and y = x2 where x is from 0 to 2.
    but then ry turns out to be 0.

    I am not sure how I would do this, most of the problems I have done are z as a function of x and y, but this case z is given but I don't know what to do with it.

    Could some one please help me with this? Thank you for your help in advance.
     
  2. jcsd
  3. Feb 11, 2010 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Unless you are describing a surface of revolution, which you haven't described, I don't see why you would involve trig functions in the parameterization. The surface y = x2 is a cylindrical parabola standing vertically on the xy plane. If I understand your description correctly, you are talking about that portion of the cylindrical surface in the first octant under the plane z = x.

    If I'm correct, the natural paramaterization would be to use x and z:

    [tex]\vec R(x,z) = \langle x,x^2,z\rangle[/tex]

    and your domain is a triangle in the xz plane. Try that.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Surface area of smooth parametric surface
Loading...