Integrating Norm in Unit Ball in Rn-2

In summary, "Integrating Norm in Unit Ball in Rn-2" is a mathematical concept that involves finding the integral of a function within a specific region in a multi-dimensional space known as Rn-2. This region is defined as the unit ball, which is a sphere with a radius of 1 centered at the origin. This concept is important in various fields of science and engineering, and is useful in solving optimization problems and analyzing the behavior of systems. In this context, the norm is defined as the distance or magnitude of a vector from the origin, and can be visualized as a sphere in 2 and 3 dimensions. This concept has applications in fields such as physics, engineering, and computer science, as well
  • #1
Matthollyw00d
92
0
[tex]\int[/tex]|x|2 with respect to the vector x in the unit ball in Rn-2

I'm dealing with volumes of unit balls in Rn and after applying a change of variable to the last 2 components and Fubini's Theorem, I get that integral and can't find a way to integrate it. Any help on this?
 
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  • #2
Generalized spherical coordinates.
 
  • #3
Would that just make |x|2=r2? I've never worked with generalized spherical coordinates before, so could you elaborate a bit?
 
  • #4
Nevermind, I found an alternate way.
 

FAQ: Integrating Norm in Unit Ball in Rn-2

What is "Integrating Norm in Unit Ball in Rn-2"?

"Integrating Norm in Unit Ball in Rn-2" is a mathematical concept that involves finding the integral, or area under the curve, of a function within a specific region in a multi-dimensional space known as Rn-2. This region is defined as the unit ball, which is a sphere with a radius of 1 centered at the origin.

Why is integrating norm in unit ball in Rn-2 important?

This concept is important in various fields of science and engineering, particularly in the study of vector spaces and functional analysis. It allows us to measure the size or magnitude of a vector in a multi-dimensional space, and is useful in solving optimization problems and analyzing the behavior of systems.

How is the norm defined in this context?

In this context, the norm is defined as the distance of a vector from the origin, or its magnitude. It is calculated using the Pythagorean theorem in 2-dimensional spaces, and can be extended to higher dimensions using the Euclidean distance formula.

Can the unit ball in Rn-2 be visualized?

Yes, the unit ball in Rn-2 can be visualized in 2 and 3 dimensions as a sphere with a radius of 1 centered at the origin. However, it becomes difficult to visualize in higher dimensions, but the concept still applies.

What are some applications of integrating norm in unit ball in Rn-2?

This concept has various applications in fields such as physics, engineering, and computer science. It is used in optimization problems, image processing, machine learning, and signal processing, to name a few. It also has applications in understanding the behavior of systems in economics, biology, and social sciences.

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