Why Replace u with Positive s in Integral Manipulation?

In summary, the conversation discusses a student's confusion with a lecturer's use of a dummy variable in manipulating an integral. The student is unsure why the lecturer replaced u with a positive s instead of a negative s at the end. The expert summarizes that both u and s are dummy variables and it does not matter what letter is used. The lecturer may have used s at the end because it was the initial dummy variable. Ultimately, once the integral is evaluated, neither s nor u will appear.
  • #1
Woolyabyss
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I was looking over my lectures notes and became stumped when the lecturer began manipulating an integral using a dummy variable. I've attached the integral below as a JPEG. I can follow the substitution up until the very end but am having trouble understanding why he replaced u with a positive s and not a negative s at the end.
Any help would be appreciated.
 

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  • #2
u and s are dummy variables for the integral. It doesn't matter what letter is used. I suppose he used s at the end, since the dummy at the beginning was s. Once the integral is evaluated neither s or u will appear.
 
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FAQ: Why Replace u with Positive s in Integral Manipulation?

What is meant by manipulation of integral limits?

Manipulation of integral limits refers to the process of changing the upper and lower bounds of an integral, while still maintaining the same value of the integral. This can be done through various methods, such as substitution or integration by parts.

Why do we need to manipulate integral limits?

Manipulating integral limits allows us to evaluate integrals that may be difficult or impossible to solve with the original limits. It also allows us to change the form of the integral to make it easier to solve or to apply different integration techniques.

How do we manipulate integral limits?

There are several techniques for manipulating integral limits, including substitution, integration by parts, and using trigonometric identities. The method used will depend on the specific integral and the desired outcome.

What are the benefits of manipulating integral limits?

The main benefit of manipulating integral limits is that it allows us to evaluate integrals that may have been impossible to solve with the original limits. It also allows us to change the form of the integral to make it easier to solve or to apply different integration techniques.

Are there any limitations to manipulating integral limits?

While manipulating integral limits can be a useful tool in solving integrals, it is not always possible to do so. Some integrals may not have a form that can be easily manipulated, and in some cases, manipulating the limits may not result in a simpler integral.

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