Results 1 to 3 of 3

Math Help - Triple integral

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    54

    Triple integral

    How to evaluate the triple integral where is the solid tetrahedon with vertices ?
    thankyou!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2008
    Posts
    903
    Here's a similar problem although the points in that post aren't showing up but still it's the same: you first have to calculate a normal to the plane you're integrating under, then derive the equation of the plane, then integrate over the appropriate region in the x-y plane.

    http://www.mathhelpforum.com/math-he...trahedron.html
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Aug 2008
    Posts
    903
    Maybe we should work this one through since it's been asked a few times. Using the plot below which is a little hard to visualize unless you can rotate it, I'll calculate two vectors: One goes from the point at (0,3,0) to (0,0,2) and the other goes from (8,0,0) to (0,3,0):

    v_1=<0,3,0>-<8,0,0>=<-8,3,0>

    v_2=<0,0,2>-<0,3,0>=<0,-3,2>

    In order to calculate a normal to the blue surface, I calculate the cross-product of these two vectors which I've indicated as the line eminating from the origin.

    \left|\begin{array}{ccc} i & j & k \\<br />
                        -8 & 3 & 0 \\<br />
                        0 & -3 & 2<br />
                        \end{array}\right|

    n=6i+16j+24k

    I can now derive the equation of the blue surface using the equation of the plane passing through the point (0,3,0) and the normal vector:

    n_x(x-p_x)+n_y(y-p_y)+n_z(z-p_z)=0

    6(x-0)+16(y-3)+24(z-0)=0

    or: z=f(x,y)=\frac{-6x-16(y-3)}{24}

    That line in the back is y=-3/8x+3 right?

    So then the integral is:

    V=\int_0^8\int_0^{-3/8x+3}\int_0^{f(x,y)} xydzdydx

    Pretty sure anyway.
    Attached Thumbnails Attached Thumbnails Triple integral-tetra2.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Double Integral and Triple Integral question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 3rd 2010, 01:47 PM
  2. Triple Integral
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 17th 2010, 09:11 AM
  3. Triple Integral
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 17th 2009, 09:13 PM
  4. triple integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 1st 2009, 06:05 PM
  5. Triple integral take 2
    Posted in the Calculus Forum
    Replies: 9
    Last Post: April 25th 2009, 11:38 AM

Search Tags


/mathhelpforum @mathhelpforum