Using Cauchy's Tip for Changing Integral Variable Inconsistencies

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Homework Help Overview

The discussion revolves around changing the variable of integration in an integral, specifically using the substitution \( w = jx \). Participants are examining inconsistencies between their results and those presented in a reference text, particularly regarding the bounds of the integral.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the application of Cauchy's theorem in relation to the variable change and the resulting bounds of integration. There is also discussion about potential typos in the reference material and whether certain steps have been omitted in the original poster's approach.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the use of Cauchy's theorem and its implications for the integral's bounds. Some guidance has been offered regarding the limits of integration, but there is no explicit consensus on the correct approach or resolution of the inconsistencies.

Contextual Notes

There are indications of potential typos in the reference material and a lack of clarity in the original poster's understanding of the steps involved in applying the theorem. The discussion highlights the need for careful consideration of the bounds when changing variables in integrals.

baby_1
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Homework Statement


I want to change integral variable to jx it means (w=jx)
9355588700_1470901837.png


Homework Equations

The Attempt at a Solution


3381303200_1470901807.jpg

but as you see the bounds of integral are different from the book text , what is my mistake?
 
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hat about the part that says: "by using the Cauchy theorem and showing that..."?
 
dear Simon
I didn't understand how can I use the Cauchy tip to solve this inconsistency?
 
It's a step you seemto have left out though.
I'll agree it looks like there's a minus sign missing. Maybe there's a typo? I can't actually read the image properly.
 
baby_1 said:
dear Simon
I didn't understand how can I use the Cauchy tip to solve this inconsistency?

It allows you to perform the integral from \omega = -i\infty to \omega = +i\infty, which on setting \omega = ix becomes x = -\infty to x = \infty.
 

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