Results 1 to 4 of 4

Math Help - Surface Integral Help

  1. #1
    Junior Member
    Joined
    Mar 2009
    Posts
    63

    Surface Integral Help

    The figure shows the surface created when the cylinder\ y^2 + z^2 = 1\ intersects\ the\ cylinder\ x^2 + z^2 = 1\ Find\ the\ area\ of\ this\ surface.

    I think to find the surface integral we need to do the double integral of ru cross rv, with respect to du and dv respectively. However, im not even sure how to get to that point.
    Attached Thumbnails Attached Thumbnails Surface Integral Help-surface.gif  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2008
    Posts
    903
    How about doing the red part below and multiplying by 16 right? You could work through the cross product but that's not necessary. Just use the formula:

    S=\mathop\int\int\limits_{\hspace{-15pt}R} \sqrt{(f_x)^2+(f_y)^2+1} dy dx

    and that red one is z=f(x,y)=\sqrt{1-x^2} and you can figure out R by equating 1-y^2=1-x^2 so y=x. So it's just that triangular region in the x-y plane above the red surface.
    Attached Thumbnails Attached Thumbnails Surface Integral Help-cylinderproblem.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2009
    Posts
    63
    Quick question, where did you get 16 from? That is the answer, but im not seeing how you came up with that.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Aug 2008
    Posts
    903
    Well, you have 8 red pieces on top as you go around right? And then eight more on the bottom.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Volume integral to a surface integral ... divergence theorem
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: October 7th 2010, 07:11 PM
  2. The integral surface 2
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 26th 2009, 04:50 PM
  3. The integral surface
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 26th 2009, 04:44 PM
  4. Surface Integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 19th 2009, 01:04 PM
  5. Surface Integral Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 14th 2008, 04:13 AM

Search Tags


/mathhelpforum @mathhelpforum