Clarification about Integration

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In summary, the conversation is about a question regarding the evaluation of an integral involving the area within a circle that is offset from the y-axis by a value R2 and has a radius of R1. The talk also mentions the need for a diagram and clarification on whether this is a homework question or for research purposes.
  • #1
Mark_ca_101
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Hello,
I am new to the forum and need some help understanding how to evaluate this integral symbolically.

∫∫ r dA

The differential element lies within a circle that is offset from the y-axis by some value R2, and the radius of the circle is R1. Again, the circle center location is (0,R2).

Any help would be greatly appreciated.
 
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  • #2
Mark_ca_101 said:
Hello,
I am new to the forum and need some help understanding how to evaluate this integral symbolically.

∫∫ r dA

The differential element lies within a circle that is offset from the y-axis by some value R2, and the radius of the circle is R1. Again, the circle center location is (0,R2).

Any help would be greatly appreciated.
Welcome to the PF, Mark.

Can you please explain this question a bit better and Upload a diagram of the geometry? Also, is this a question for your schoolwork? If so, I can move it to the Homework Help forums as long as you show your initial work toward the solution. :smile:
 
  • #3
berkeman said:
Welcome to the PF, Mark.

Can you please explain this question a bit better and Upload a diagram of the geometry? Also, is this a question for your schoolwork? If so, I can move it to the Homework Help forums as long as you show your initial work toward the solution. :smile:

berkeman,

This is not a homework problem, this is for research.

I want to calculate the angular momentum induced by introducing flow into a cylinder by an offset, inclined tube. I have referenced a journal paper regarding this method, but I'm not clear on how they are integrating this area. Please see the diagram below.

For simplicity reasons, the S1 area is shown as a circle, while it would actually be an ellipse.[PLAIN]https://www.physicsforums.com/attachments/da-png.113264/[PLAIN]https://www.physicsforums.com/attachments/inflow-angular-momentum-png.113265/
 
Last edited by a moderator:
  • #4
Mark_ca_101 said:
berkeman,

This is not a homework problem, this is for research.

I want to calculate the angular momentum induced by introducing flow into a cylinder by an offset, inclined tube. I have referenced a journal paper regarding this method, but I'm not clear on how they are integrating this area. Please see the diagram below.

For simplicity reasons, the S1 area is shown as a circle, while it would actually be an ellipse.[PLAIN]https://www.physicsforums.com/attachments/da-png.113264/[PLAIN]https://www.physicsforums.com/attachments/inflow-angular-momentum-png.113265/[/QUOTE]
dA.png
inflow - angular momentum.png
 
Last edited by a moderator:

What is integration?

Integration is a mathematical process that involves finding the area under a curve. It is used to solve problems related to motion, volume, and other real-world applications.

Why is integration important?

Integration is important because it provides a way to solve complex problems that cannot be solved by traditional algebraic methods. It is also used in many scientific and engineering fields to model and analyze real-world phenomena.

What are the different types of integration?

The two main types of integration are definite and indefinite integration. Definite integration involves finding the exact numerical value of the area under a curve within a given interval, while indefinite integration involves finding the antiderivative of a function.

What is the difference between integration and differentiation?

Integration and differentiation are inverse operations. While differentiation involves finding the rate of change of a function, integration involves finding the original function from its derivative. In other words, integration "undoes" differentiation.

How is integration used in real life?

Integration has many real-life applications, such as in physics to calculate the work done by a force, in economics to calculate the total revenue of a company, and in medicine to model drug concentration in the body. It is also used in computer science to simulate and analyze complex systems.

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