Please explain how this integration is done

In summary, integration in science is the process of combining different elements or systems to create a unified understanding of a topic. It is important in science because it allows for the development of more accurate theories and models and for making connections between different areas of research. Integration is done through analyzing and synthesizing data, identifying common patterns, and collaborating with scientists from different fields. Challenges in integration include conflicting data and the need for effective communication. However, integration can benefit scientific progress by leading to new technologies and solutions, as well as identifying gaps in knowledge for future research.
  • #1
bksree
77
2
Hi
Attached is an extract of a paper by Lord Rayleigh on pressure generated during collapse of a bubble in a liquid. Will someone please explain how the RHS of equation (2) in the attachment is obtained ?

TIA
 

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  • #2
Use eq (1) to Substitute [itex] \frac{UR^2}{r^2} [/itex] for [itex] u [/itex] in the integral. Doesn't the integration work out after that?
 
  • #3
Stephen
Thank you. Got it now. On hindsight, what a silly question to ask.

Thanks again
 

1. What is integration?

Integration is the process of combining different elements or systems together to create a unified whole. In the context of science, integration can refer to the incorporation of new data or concepts into existing theories or models.

2. Why is integration important in science?

Integration allows scientists to make connections between different areas of research and to create a more comprehensive understanding of a particular topic. It also allows for the development of more accurate and complete theories and models.

3. How is integration done in science?

The process of integration in science involves analyzing and synthesizing data from different sources, identifying common patterns and themes, and incorporating them into existing theories or models. This can also involve collaboration and communication between scientists from different fields.

4. What are some challenges in integrating different ideas in science?

One challenge in integration is the potential for conflicting data or theories, which may require further research or refinement to resolve. Another challenge is the need for effective communication and collaboration between scientists from different disciplines, which can be hindered by differences in terminology or approaches.

5. How can integration benefit scientific progress?

By integrating different ideas and data, scientists can develop more accurate and comprehensive understandings of complex phenomena. This can lead to the development of new technologies, treatments, and solutions to real-world problems. Integration also allows for the identification of gaps in current knowledge, which can guide future research and advancements in the field.

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