1. Limited time only! Sign up for a free 30min personal 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!

Evaluate triple integral

  1. Nov 8, 2012 #1
    1. The problem statement, all variables and given/known data

    Evaluate triple integral

    z^2 dxdydz

    throughout
    i) the part of the sphere x^2 + y^2 + z^2 = a^2 (first octant)
    ii)the complete interior of the sphere x^2 + y^2 + z^2 = a^2 (first octant)


    2. Relevant equations

    It is probably good idea to work in spherical coords.

    z = r*cosφ
    x = r*sinφ cosθ
    y = r*sinφ sinθ

    dxdydz = r^2 sinφ drdφdθ

    3. The attempt at a solution

    I'l start at part ii) because its the part I can do.
    Here the boundaries are:
    0 =< r < a
    0 =< φ < pi/2
    0 =< θ < pi/2

    the integration now becomes:

    (Int[r=0, a] r^4 dr )( Int[φ=0, pi/2] sinφcos^2 φ)( Int [θ=0, pi/2]) = r^5/30 * pi

    i) But for part i), I am confused. The integral should be evaluated only on the surface of the sphere. The radius a is constant in length, so how should r be defined?
    a < r < a, makes no sense.

    Need advice.
     
    Last edited: Nov 8, 2012
  2. jcsd
  3. Nov 8, 2012 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Are you sure the problem is quoted correctly?
     
  4. Nov 8, 2012 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Part i obviously means the interior of the sphere in the first octant. Otherwise it wouldn't be a triple integral.
     
  5. Nov 9, 2012 #4
    You are right, I understand what nonsense I was thinking about. The part i) is not quoted correctly. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Evaluate triple integral
Loading...