Results 1 to 2 of 2

Thread: Mass Triple Integrals

  1. #1
    Sep 2008

    Mass Triple Integrals

    Find the mass of the solid region bounded by the planes
    x-z = -1
    and the surface

    The density of the solid is (x,y,z)=2y+5

    My analytic geometry skills are a little lost. Could someone please remind me how to graph these planes so I can find the limits for my integrals?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Aug 2008
    Hi. Use Mathematica to draw it. Oh I realize that's a lazy approach and cuts into your analytical education but if you're having problems visualizing it, then first get it (Mathematica), then figure out how the three equations give rise to the surfaces: Red is x+z=1, Blue is x-z=-1, and Green is y=Sqrt[z]. Now, in general, a triple integral is:

    $\displaystyle \int_a^b\int_{y=f_1(x)}^{y=f_2(z)}\int_{z=g(x,y)}^ {z=h(x,y)} u(x,y,z) dzdydx$

    so that's up from the surface g to the surface h, bordered in the x-y plane between the functions f1 and f2, and then finally in the range of x from a to b.

    So we want that tee-pee volume in there right and it's symmetrical to the z-x plane since u=2y+5 so take half and multiply by two. So we go up from z=y^2 to the red sheet z=1-x and the foot-print in the x-y plane is when the two equations y=Sqrt[z] and x+1=z are satisfied (the red and green surfaces intersect or x=y^2-1. So integrating in the order dzdxdy, I get:

    $\displaystyle 2\int_0^1\int_0^{y^2-1}\int_{y^2}^{1-x} (2y+5)dzdxdy$

    but I'm not sure about it so you go over it and see if I missed it.
    Attached Thumbnails Attached Thumbnails Mass Triple Integrals-tee-tee-volume.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Nov 18th 2010, 06:04 AM
  2. triple integral and center of mass
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Dec 20th 2009, 07:39 AM
  3. Replies: 1
    Last Post: Nov 15th 2009, 05:04 PM
  4. Replies: 1
    Last Post: Nov 4th 2009, 03:55 AM
  5. triple integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Mar 4th 2009, 11:20 PM

Search Tags

/mathhelpforum @mathhelpforum