Recasting integration variable

[maddav]

Homework Statement

Recast the integration variable of the following integral to da

$$\tau$$=$$\int$$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.

 

[tiny-tim]

Welcome to PF!

Hi maddav! Welcome to PF!

Recast the integration variable of the following integral to da

$$\tau$$=$$\int$$k dr

k is a positive constant
…
dr= c*dt/a

Do you mean dt rather than da?

If not, can you tell us the bigger problem, so we can see what it all means?

 

[HallsofIvy]

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.

 

[maddav]

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!