Trying to understand an integration example

In summary, there was a conversation about an integration example and the use of a substitution. The first person asked for help understanding the process, specifically how the substitution results in 1/(√2 ΔRP) dx. The second person explained that the substitution is made to make the process easier, and then provided the derivative of the substitution with respect to x, which leads to the result of dx = (√2 ΔRP) da. The first person thanked the second person and stated they would review the explanation.
  • #1
OnceMore
23
1
Hello.

I am having some trouble understanding an integration example we have. I have written it out in the attached pdf. I would be grateful if someone can help me undertand what is going on.

I assume you let a = (x-RP)/(√2 ΔRP) da to make the process easier, but I am, not sure how that becomes

1/(√2 ΔRP) dx

I thought if we took the top line to be a constant, that should have come out as zero?

-S
 

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  • #2
You make the substitution a = (x-RP)/(√2 ΔRP) , then take the derivative of this with respect to x. Everything but x is treated as a constant, so this gives
da/dx = 1/(√2 ΔRP), or dx = (√2 ΔRP) da.
 
  • #3
Hello,

Thanks for the reply. Right, yea, I think I understand that ...I will run through it a few times just to make sure.

Thanks.

-S
 

FAQ: Trying to understand an integration example

What is integration?

Integration is the process of combining different parts or elements into a whole. In the context of science, integration involves combining information, data, or theories from different disciplines to gain a better understanding of a concept or phenomenon.

Why is understanding integration important?

Understanding integration allows scientists to make connections between seemingly unrelated concepts and to build a more comprehensive understanding of a particular topic. It also promotes collaboration and innovation by bringing together diverse perspectives and expertise.

What are some examples of integration in science?

Examples of integration in science include using data from multiple sources to create a more accurate model, combining theories from different fields to explain a phenomenon, and incorporating findings from various experiments to support a hypothesis.

What are the steps involved in integrating information?

The steps involved in integrating information may vary depending on the specific context, but generally include identifying the relevant information, evaluating its validity and reliability, and synthesizing it into a coherent understanding. This may also involve identifying gaps in knowledge and conducting further research to address them.

How can scientists improve their integration skills?

Scientists can improve their integration skills by actively seeking out information and perspectives from different disciplines, engaging in interdisciplinary collaborations, and continuously evaluating and refining their understanding of a topic. Developing critical thinking and analytical skills can also aid in the process of integrating information.

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