Volume under a surface which is cut by a circle

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Discussion Overview

The discussion revolves around calculating the average value of a function that depends on the variable z over a circular area in the zx-plane. Participants are exploring the formulation of the integral needed for this calculation, clarifying the relationship between the variables involved.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant seeks help in formulating an integral for the average value of a function f(z) over a circle in the zx-plane, centered at z=100 with a radius of 50.
  • Another participant questions the connection between the z-value and the circular area in the xy-plane, suggesting a need for clarification on how z relates to x and y.
  • A later reply points out that referring to a center "at z=100" in the zx-plane is problematic, as it describes a line rather than a point.
  • One participant asks if the original poster knows how to find the average value of a function over a domain, implying that this is a necessary step in addressing the problem.

Areas of Agreement / Disagreement

Participants express confusion over the original question's formulation and the relationship between the variables, indicating that there is no consensus on how to approach the problem.

Contextual Notes

There are unresolved questions regarding the definitions of the variables and the geometric interpretation of the average value calculation in the zx-plane.

Skorpan
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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.
 
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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?
 
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 let's say z=100 with a radius of 50. so that the values from the function close to z=100 gets a higher importance.
 
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.
 
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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