Vector Integration Prove: Int over Closed S=0

aj06 · 2010-03-20T04:53:34+00:00

Prove \int\int_{S}r \times dS=0 for any closed surface S.

Thread starter aj06
Start date Mar 19, 2010
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Integration Vector

In summary, vector integration is a mathematical technique used to integrate vector-valued functions by finding the area under a curve in a multi-dimensional space. It involves using the notation "Int over Closed S=0" to indicate that the integral over a closed surface is equal to zero. The proof of vector integration involves using line integrals, flux integrals, and the divergence theorem. It is important in various fields such as physics, fluid mechanics, and electromagnetism, allowing for the calculation of important quantities like work, flow, and flux. Vector integration is also applicable in real-world situations and has many practical applications.

Mar 19, 2010

aj06

Prove [tex]\int\int_{S}r \times dS=0[/tex]
for any closed surface S.

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Mar 20, 2010

Dustinsfl

This should probably be posted in Calculus and beyond.

1. What is vector integration?

Vector integration is a mathematical technique used to integrate vector-valued functions. It involves finding the area under a curve in a multi-dimensional space.

2. What does "Int over Closed S=0" mean?

"Int over Closed S=0" is a notation used in vector integration to indicate that the integral over a closed surface is equal to zero. This means that the net flow of the vector field through the surface is equal to zero.

3. How is vector integration proved?

Vector integration is proved using a combination of mathematical techniques, including line integrals, flux integrals, and the divergence theorem. The specific proof may vary depending on the problem at hand.

4. What is the importance of vector integration?

Vector integration is important in many areas of science and engineering, including physics, fluid mechanics, and electromagnetism. It allows us to calculate important quantities such as work, flow, and flux in a variety of contexts.

5. Can vector integration be applied in real-world situations?

Yes, vector integration can be applied in real-world situations to solve a variety of problems. For example, it can be used to calculate the work done by a force on an object, or the flow of a fluid through a surface. It is a powerful tool that has many practical applications.