Approximation question -- How does this approximation simplify the integral?

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Homework Help Overview

The discussion revolves around an approximation related to simplifying an integral, likely within the context of calculus or mathematical physics. Participants are examining the implications of this approximation on the integral's evaluation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the role of specific variables in the integral, such as lambda and k_z, and discussing the conditions under which the approximation holds, including the significance of evaluating at the midpoint and the implications of the parameters l, lambda, and k_z.

Discussion Status

The discussion is active, with participants exploring the rationale behind the approximation and its assumptions. Some guidance has been offered regarding the evaluation method, but multiple interpretations and questions remain open.

Contextual Notes

There are constraints mentioned regarding the relationships between the parameters l, lambda, and k_z, specifically the conditions l << lambda and k_z << pi, which are under scrutiny.

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how does this aproximation reduse the integral
upload_2014-12-5_1-47-46.png
 
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Where are lambda and k_z in the integral?

The approximation simply assumes the integrand to be constant, evaluates it at the midpoint (z'=0) and multiplies it with the range z' takes.
 
so its because r'=0 ??
then why we need
l<<lambda kz<<pi
?
 
The exponential function should not change its argument too much, so kzl/r should be small compared to 1.
 

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