Results 1 to 2 of 2

Math Help - Help with setting up bonds in a triple integral

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    4

    Help with setting up bonds in a triple integral

    Hi,

    Here is the problem i am working on...
    evaluate the triple integral ∫ xy dV where E is the solid tetrahedron with vertices (0,0,0), (6,0,0), (0,1,0) and (0,0,7).

    I sketched the region and got the following limits..
    for x--- x=0 to x=6(1-y)
    for y- - - y=0 to y=1
    for z----z= 0 to z= 7(1-x/6-y)

    i evaluated the integral with the order of integration dzdxdy and i got 15 but it's wrong.

    can someone explain me if my bouds or order of integtation are wrong,
    thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by Candy21 View Post
    Hi,

    Here is the problem i am working on...
    evaluate the triple integral ∫ xy dV where E is the solid tetrahedron with vertices (0,0,0), (6,0,0), (0,1,0) and (0,0,7).

    I sketched the region and got the following limits..
    for x--- x=0 to x=6(1-y)
    for y- - - y=0 to y=1
    for z----z= 0 to z= 7(1-x/6-y)

    i evaluated the integral with the order of integration dzdxdy (Everything is correct up to here!) and i got 15 but it's wrong.

    can someone explain me if my bounds or order of integration are wrong,
    thank you
    The integral is \int_0^1\!\!\!\int_0^{6(1-y)}\!\!\!\int_0^{7(1-\frac x6 - y)}\!\!\!xy\,dzdxdy = \int_0^1\!\!\!\int_0^{6(1-y)}\!\!\!7\bigl(1-\tfrac x6 - y\bigr)xy\,dxdy. After doing the x-integral, I get \int_0^1\!\!\!42y(1-y)^3\,dy = \frac{21}{10}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 18th 2010, 06:04 AM
  2. Need some help setting up a triple integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 13th 2010, 06:05 PM
  3. Replies: 3
    Last Post: July 6th 2010, 01:00 PM
  4. Setting up triple integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 11th 2009, 03:45 AM
  5. setting up a triple integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 5th 2009, 05:56 PM

Search Tags


/mathhelpforum @mathhelpforum