1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Parametrization of a surface

  1. Mar 24, 2016 #1
    An area A in the (x,y) plane is limited by the y-axis and a parabola with the equation x=6-y^2. Further, is a surface F given by the part of the graph for the function h(x,y)=6-x-y^2 which satisfies the conditions x>=0 and z>=0.

    Determine a parametrization for A and for F.

    So far i've got the parametrization for A, which i got to r(u,v)=(6-v^2,v), v ∈ [0,6].

    My attempt of a solution for F is r(u,v)=(u,v, 6-u-v^2), but i am not sure about the limits of each parameter and if it's the correct parametrization. Could someone help me out?

  2. jcsd
  3. Mar 24, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    First, let's talk about F. I agree with what you have done, but I don't see any reason to rename the parameters so I would have written$$
    \vec r(x,y) = \langle x,y,6-x-y^2\rangle$$Your parameterization for A isn't correct because it has only one variable, thus describing a curve instead of an area. The easy way to parameterize A would be just to take the z coordinate equal zero in the parameterization of the surface. Using a different letter that would give$$
    \vec R(x,y) = \langle x,y,0\rangle$$I know, that doesn't seem correct because x and y could vary all over the place, which brings us to your original question: what are the limits? Well, what limits would you use for a double intgral over that xy region if you were calculating its area? You will find your answer there.
    Last edited: Mar 24, 2016
  4. Mar 25, 2016 #3
    Thanks a lot for your reply and help!

    I think i got it now :) I got a new problem now, i'll have to find the volume between those two parameterizations, but i'll let my brain struggle with that one for a bit longer.

    Take care!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted