Question about Legendre elliptic integrals

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    Integrals Legendre
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Homework Help Overview

The discussion revolves around Legendre elliptic integrals, specifically the transformation of variables in the context of an integral involving parameters a, b, and c. The original poster expresses confusion regarding a substitution step in the integral's evaluation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster questions the reasoning behind the variable substitution x=a+(b-a)t and its implications for understanding similar problems. Some participants suggest a more lighthearted approach to the confusion, while others reflect on their own experiences with the material.

Discussion Status

The discussion appears to be ongoing, with participants sharing their thoughts and experiences related to the topic. While some guidance is implied, there is no clear consensus on the reasoning behind the substitution or its broader applicability.

Contextual Notes

The original poster mentions a desire for logical reasoning behind the substitution, indicating a potential gap in understanding foundational concepts. There is also a reference to personal struggles with the course material and a plan to seek additional resources over the summer.

mercenarycor
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Homework Statement

[/B]
J(a, b, c;y)=∫aydx/√((x-a)(x-b)(x-c)), let a<b<c

Homework Equations


f(θ, k)=∫0θdx/√(1-k2sin2(x)), k≤1

The Attempt at a Solution


This is an example from my study material, and I don't understand the first step they do.
Let x=a+(b-a)t, dx=(b-a)dt
Wait...what? Why? How did they come to that decision. I hope there's a logical reason, otherwise how can I apply this to my other problems? I keep running into "make an educated guess." Is this another guess?
 
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I suggest you show a bit of unquestioning blind faith and try it.
 
And that is how we discovered the new world!
 
And that is how we discovered the new world!

No shipwrecks or monstrous squid, I take it?
 
Devoured by the Kraken, I'm afraid. Ended up dropping the course, going to spend the summer with Schaum's trying to build a better foundation for the math I need.
 

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