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Are you interesting about average value if so trying here.

  1. Nov 15, 2008 #1
    Hello

    here you have the same question in the enclosed

    What is the average value?

    average value for (exp [tex]\alpha[/tex]Z ) = [tex]\int[/tex][tex]\int[/tex] exp[tex]\alpha[/tex]Z ds / [tex]\int[/tex][tex]\int[/tex] ds



    Over the sphere S: X^2+Y^2+Z^2=a^2

    Also by use the parameterization

    X= a sinϴ cos ɸ
    Y= a sinϴ sin ɸ
    Z= a cos ϴ

    And the usual substitution t = cos ϴ in the integral:

    [tex]0\int[/tex][tex]\Pi[/tex] f (cos ϴ) sinϴ dϴ =[tex]-1\int[/tex]1 f(t) dt

    Thanks
     
    Last edited: Nov 25, 2008
  2. jcsd
  3. Nov 16, 2008 #2
    No comments or solution until now!!!

     
  4. Nov 16, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Again, Word files are notorious for harboring viruses. I will not open one from someone I do not know.
     
  5. Nov 16, 2008 #4
    Hello here the same question in the enclosed

    What is the average value?

    average value for (exp [tex]\alpha[/tex]Z ) = [tex]\int[/tex][tex]\int[/tex] exp[tex]\alpha[/tex]Z ds / [tex]\int[/tex][tex]\int[/tex] ds



    Over the sphere S: X^2+Y^2+Z^2=a^2

    Also by use the parameterization

    X= a sinϴ cos ɸ
    Y= a sinϴ sin ɸ
    Z= a cos ϴ

    And the usual substitution t = cos ϴ in the integral:

    [tex]0\int[/tex][tex]\Pi[/tex] f (cos ϴ) sinϴ dϴ =[tex]-1\int[/tex]1 f(t) dt

    Thanks
     
  6. Nov 18, 2008 #5
    I can kind of guess what you mean, but your notation is pretty bad. I do not know what exp[tex]\:^\alpha Z[/tex] is supposed to be. Your substitution seems wrong, your notation is unorthodox and you write factors like -1 instead of just a - . This is probably the reason why people don't answer.

    You might have better chances if you wrote something like:

    "I am trying to get the average [tex]\left< f(z) \right>_{S_a}[/tex] of a function [tex]f(z)= \alpha ^ z[/tex] over a sphere [tex]S_a[/tex] of radius [tex]r=\sqrt{a}[/tex]. I swear this is not for homework.

    What I have so far is this:

    [tex]\left< f(z) \right>_{S_a} = \frac{\int_{S_a} \alpha^z\,\mathrm{d}\Omega}{\int_{S_a} \,\mathrm{d}\Omega}[/tex]

    I tried to express the integral in polar coordinates:
    X= a sinϴ cos ɸ
    Y= a sinϴ sin ɸ
    Z= a cos ϴ
    [tex]\theta \in \left[0,\pi \right][/tex]
    [tex]\phi \in \left[0,2\pi \right][/tex]

    and found:
    [tex] \int_{S_a} f(z) \,\mathrm{d}\Omega = \int_0^{\pi} f(\cos \theta) \sin \theta \, \mathrm{d}\theta [/tex]

    Is this correct? How do I proceed?"

    Then people would have told you what you did wrong.
     
  7. Nov 24, 2008 #6
    Thanks for reply but it is not correct hint and I think you don’t proceed with the right way for the real problem you probably fix some thing else many things missing from the real posted thank you
     
    Last edited by a moderator: Nov 26, 2008
  8. Nov 24, 2008 #7
    Re: Are you interesting about average value if so trying here.ENGINEERING MATHEMATICS

    YES memomath I belive there are some mistakes and the good hint to the correct answer for this problem would be in ENGINEERING MATHEMATICS JOHN BIRD

     
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