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Volume under a surface which is cut by a circle

  1. Dec 10, 2007 #1
    Hi!

    I have a function that only depends on z. It is homogeneous in both x and y direction. Then at a certain z-value I need the average value in a circle with radius r from this point. The circle is in the x-plane. How should my integral look like?

    Thanks to anyone that can help me.
     
  2. jcsd
  3. Dec 10, 2007 #2

    HallsofIvy

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    I assume you mean the xy-plane! I'm not clear on what you mean by "at a certain z value" and then have a circle in the xy-plane, with radius r "from this point". How is the point in the xy-plane connected with a z value?

    It looks to me like you want the double integral, over a disk in the plane, of f(z). But how is z connected to x and y?
     
  4. Dec 10, 2007 #3
    I have a function f(z). Then i would like to have the average value of this function from a circle in the z-x plane. the centre of the circle should be at lets say z=100 with a radius of 50. so that the values from the function close to z=100 gets a higher importance.
     
  5. Dec 10, 2007 #4

    HallsofIvy

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    OH! zx- plane! Now the problem is that it makes no sense to say the center "is at z= 100" since that is a line in the zx-plane, not a point.
     
  6. Dec 10, 2007 #5
    do you know how to find the average value of a function over a domain? cause that sounds exactly like what you want to do
     
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