Results 1 to 2 of 2

Math Help - The region 0 < x < y < z < 1

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    48

    The region 0 < x < y < z < 1

    I need to integrate over the region in the title 0 < x < y < z < 1.

    Am I correct in understanding that this is the region in x,y,z-space in the first octant with vertex interceptions at (1,0,0), (0,1,0), and (0,0,1) resembling a "pyramid"?

    But then the integral of 48*x*y*z over this region must equal one, but I am getting

    The integral from x=0 to 1, the integral from y=0 to 1-x, the integral of z=0 to 1 - x - y of 48xyz dz dy dx (this is a triple integral written in "word" form since I don't know latex.

    But my answer is 1/15, which is not correct. What am I doing wrong? Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: The region 0 < x < y < z < 1

    Quote Originally Posted by arcketer View Post
    The integral from x=0 to 1, the integral from y=0 to 1-x, the integral of z=0 to 1 - x - y of 48xyz dz dy dx (this is a triple integral written in "word" form since I don't know latex. But my answer is 1/15, which is not correct. What am I doing wrong? Thanks!
    The region is a pyramid with vertex (0,0,0),(1,1,1),(0,1,1),(0,0,1) . You'll get \iiint_{R}48xyz\;dxdydz=\int_0^1dx\int_{x}^1dy\int  _{y}^148xyz\;dz=\ldots=1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Area of a region
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 28th 2010, 08:06 AM
  2. Z-plane region
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 28th 2009, 09:45 PM
  3. How to determine pdf region
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 27th 2009, 12:57 AM
  4. Area of region
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 11th 2009, 10:30 PM
  5. region
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 23rd 2008, 06:16 PM

Search Tags


/mathhelpforum @mathhelpforum