1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Triple Integrals (volumes)

  1. Jun 14, 2009 #1
    1. The problem statement, all variables and given/known data
    A solid is definited by the inequalities 0[tex]\leq[/tex]x[tex]\leq[/tex]1, 0[tex]\leq[/tex]y[tex]\leq[/tex]1, and 0[tex]\leq[/tex]z[tex]\leq[/tex]x2+y2. The temperature of the solid is given by the function T=25-3z. Find the average temperature of the solid.


    3. The attempt at a solution

    I solved the integral, however I could not figure out how to determine what to do to find the average temperature value. In the answers i was given. They have no explanation, just the volume of solid above the inequalities is (!) 2/3.
    So they therefore times the integral by 3/2.

    Can someone please explain how this idea works? Thanks
     
  2. jcsd
  3. Jun 14, 2009 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    The average value of any function [itex]f(x,y,z)[/itex] over some volume [itex]\mathcal{V}[/itex] is, by definition;

    [tex]\langle f \rangle \equiv \frac{\int_{\mathcal{V}}f dV}{\int_{\mathcal{V}} dV}[/tex]

    ...apply that to [itex]T(z)[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Triple Integrals (volumes)
  1. Triple integral volume (Replies: 5)

Loading...