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!

Parameterizing surface in surface integral problem

  1. Sep 18, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the area of the surface cut from the paraboloid z=2x2+2y2 by the planes z=2 and z=8.


    2. Relevant equations
    Surface area of S= ∫∫ ||Ts×Tt|| ds dt


    3. The attempt at a solution
    What I am really having trouble doing in this problem (and in general) is parameterizing the surface in terms of s and t. I think for this surface an accurate parameterization is (s,t,√(2s2+2t2)) but I am not sure. Also, I wouldn't know how the planes cutting the paraboloid would come into play.
     
  2. jcsd
  3. Sep 18, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Why did you put the square root into (s,t,√(2s^2+2t^2)) for a starting point? The planes will define the (s,t) region you will integrate over.
     
  4. Sep 18, 2012 #3
    Good question. I seem to have made an error. I was looking at the parameterization of a different paraboloid and must have gotten mixed up.
     
  5. Sep 18, 2012 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Ok, so just use (s,t,2s^2+2t^2). Now if z=2, then that means 2s^2+2t^2=2. What kind of curve is that in the (s,t) plane?
     
  6. Sep 18, 2012 #5
    A circle of radius 1. When z=8, the curve will be a circle of radius 2. Not sure where to go from here.
     
  7. Sep 18, 2012 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Ok again. So you are going integrate between those two circles. Suggests you might think about polar coordinates. I'm not sure why you are not sure where to go. The next thing would be to work on what to integrate, right? Try working on the partial derivative vectors and finding the cross product.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Parameterizing surface in surface integral problem
Loading...