Results 1 to 3 of 3

Math Help - Need help with the boundaries of a 3D solid

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    25

    Need help with the boundaries of a 3D solid

    How do you find the boundaries of a volume defined by
    -1\leq x+y+3z\leq 1
    1\leq 2y-z\leq 7
     -1\leq x+y\leq 1

    to compute  \int\int\int 9z^2 dxdydz
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Various ways. Projection is one such way.

    Simply eliminate all the 'z's and see wht it looks like from the point of view of the x-y plane.

    Do the same for x-z and y-z.

    Are you sure you must use dxdydz? Often there is one way that is easier than another. Maybe dydzdx would be more straight-forward. You must keep your eyes open.

    Exploit symmetries and redundancies. I don't see much in this one except that the first and third constraints are a little odd. If z > 0, does the third one mean anything? Subtract 3z in the first and compare it to the third. What does that mean?
    Last edited by TKHunny; February 13th 2010 at 12:31 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    Posts
    25
    Quote Originally Posted by TKHunny View Post
    Various ways. Projection is one such way.

    Simply eliminate all the 'z's and see wht it looks like from the point of view of the x-y plane.

    Do the same for x-z and y-z.

    Are you sure you must use dxdydz? Often there is one way that is easier than another. Maybe dydzdx would be more straight-forward. You must keep your eyes open.

    Exploit symmetries and redundancies. I don't see much in this one except that the first and third constraints are a little odd. If z > 0, does the third one mean anything? Subtract 3z in the first and compare it to the third. What does that mean?
    I used the constraints to my advantage and this is what I came up with. Can anybody confirm whether the following is correct?

    \int_{\frac{-15}{6}}^{\frac{5}{6}} \int_{\frac{3+2x}{2}}^{\frac{5+2x}{2}}\int_{\frac{-1-2x-2z}{4}}^{\frac{9-2x-2z}{4}} 9z^2 dydzdx
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Relationship of Boundaries
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: July 12th 2011, 11:56 PM
  2. PDE with moving boundaries
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: May 4th 2011, 09:40 AM
  3. Boundaries
    Posted in the Math Topics Forum
    Replies: 10
    Last Post: January 8th 2011, 12:27 PM
  4. Replies: 12
    Last Post: February 16th 2010, 04:41 PM
  5. Polar Boundaries.
    Posted in the Calculus Forum
    Replies: 6
    Last Post: October 20th 2009, 03:13 AM

Search Tags


/mathhelpforum @mathhelpforum