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: Representing a region as limits of a volume integral

  1. Aug 28, 2011 #1
    1. The problem statement, all variables and given/known data

    i have the region given as being bounded by x2+y2=4 and z=0 and z=3.
    this problem asks to prove gauss divergence theorem for a given vector F

    2. Relevant equations
    3. The attempt at a solution
    As for the volume integral, i had no problem. But for the surface integral, how many surfaces are there actually? How are the normals represented?

    I assumed it is a cylinder(Is it??).. and i got the normal vectors to the top surface and the bottom surfaces to be k and -k respectively. But these cancel out effectively. The problem here is i dont know how to represent any other surface, if any.. i really do not know to find the others. could you give me an idea on how to go about this ? i mean, finding the surfaces and limits..
  2. jcsd
  3. Aug 28, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, the side surface is a cylinder. You might parameterize the surface x2+y2 = 4 for z between 0 and 3 like this:

    R(θ,z) = <2cos(θ), 2sin(θ),z>, 0 ≤θ≤ 2pi, 0≤z≤3
  4. Aug 28, 2011 #3


    User Avatar
    Science Advisor

    There are three "sides", the cylindrical [itex]x^2+ y^2= 4[/itex] and two circular ends at z= 0 and z= 3.
    For those good parametric equations would be [itex]x= r cos(\theta)[/itex], [itex]y= r sin(\thet)[/itex], with r from 0 to 2 and [itex]\theta[/itex] from 0 to [itex]2\pi[/itex], z= 0 or 3.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook