Results 1 to 2 of 2
Like Tree2Thanks
  • 2 Post By HallsofIvy

Math Help - Changing order of triple integral?

  1. #1
    Newbie
    Joined
    Jun 2014
    From
    United States
    Posts
    1

    Changing order of triple integral?

    Changing order of triple integral?-capture.png
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,790
    Thanks
    1531

    Re: Changing order of triple integral?

    Start by draw a graph of the region of integration. The given integral has x going from 0 to 1, y going from 0 to 1, and z going from 0 to y- x. z= 0 is the xy-plane and z= y- x is also a plane that cuts the xy-plane in the line y= x. In the region 0<x< 1, 0< y< 1, that will be above the xy-plane for y> x and below it for y< x.

    In (1.) the the last, "outside", integral is with respect to dy and must have numbers as limits. What are the smallest and largest values y can take on?
    The second, "middle", integral is with respect to x. For each y, what are the smallest and largest values of x (as a function of y)?
    The third, "inner", integral is with respect to z. For each x and y, what are the smallest and largest values of z (as a function of x and y)?

    In (2.) the the last, "outside", integral is with respect to dz and must have numbers as limits. What are the smallest and largest values z can take on?
    The second, "middle", integral is with respect to x. For each z, what are the smallest and largest values of x (as a function of z)?
    The third, "inner", integral is with respect to y. For each x and z, what are the smallest and largest values of y (as a function of x and z)?
    Thanks from topsquark and catenary
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Triple integral in a new order
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 15th 2013, 06:45 PM
  2. Replies: 0
    Last Post: November 30th 2012, 02:40 PM
  3. change order of integration of triple integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 2nd 2011, 09:43 PM
  4. Replies: 2
    Last Post: December 1st 2009, 12:29 PM
  5. Changing order of integration?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 20th 2008, 01:39 PM

Search Tags


/mathhelpforum @mathhelpforum