Recasting integration variable

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Homework Help Overview

The original poster is working on a problem involving the recasting of an integration variable in an integral related to cosmology. The integral in question is expressed as τ = ∫k dr, where k is a positive constant. The poster is uncertain about the process of changing the variable to da.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the possibility of a misunderstanding regarding the variable to be recast, with one suggesting a change to dt instead of da. There is also mention of using the Friedmann equation to relate dt and da.

Discussion Status

The discussion is ongoing, with some participants providing clarifications and suggestions regarding the variable change. The original poster acknowledges a simpler nature to the problem than initially assumed, indicating a productive direction in the conversation.

Contextual Notes

The problem is part of a larger context in cosmology, and there is mention of specific assumptions regarding the universe being composed entirely of matter and a cosmological constant.

maddav
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Homework Statement



Recast the integration variable of the following integral to da

[tex]\tau[/tex]=[tex]\int[/tex]k dr

k is a positive constant

Homework Equations



dr= c*dt/a

The Attempt at a Solution



I have no idea, I'm sure it's something really simple, but I really just can't think.

btw, this is part of a bigger problem, that I know how to solve, but I've forgotten how to do this.

Thanks.
 
Last edited:
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Welcome to PF!

Hi maddav! Welcome to PF! :wink:
maddav said:
Recast the integration variable of the following integral to da

[tex]\tau[/tex]=[tex]\int[/tex]k dr

k is a positive constant

dr= c*dt/a

Do you mean dt rather than da? :confused:

If not, can you tell us the bigger problem, so we can see what it all means? :smile:
 
If, as tiny tim suggested, you meant "recast to dt", then just replace the "dr" in the integral with "cdt/a" which you say is equal to it.
 
Yeah, the problem was less mathematical than i'd assumed, it's a cosmology question, so it's fairly simple.

I initially replaced it with dt (prior to it being suggested here), but of course, I'm told that universe is entirely matter and cosmological constant, so I can just rewrite dt as da using the friedmann equation.

Thanks anyway guys!
 

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