Volume under a surface which is cut by a circle

[Skorpan]

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.

 

[HallsofIvy]

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?

 

[Skorpan]

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.

 

[HallsofIvy]

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.

 

[ice109]

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