This seems so simple, but I can't for the life of me work it out. I've forgotten a lot of maths over the years, so I need a little help.(adsbygoogle = window.adsbygoogle || []).push({});

The question goes:

Using the substitution

[tex]u=\frac{r}{R_1}[/tex]

Show that :

[tex]\int_R^{R_1} \sqrt{\frac{R_1}{r}-1} dr = \int_\frac{R}{R_1}^1 \sqrt{\frac{1}{u}-1} du[/tex]

So, the substitution under the root is easy enough, it's just the changing of the limits that I can't seem to figure out (or perhaps remember).

I got

[tex]\frac{du}{dr}=\frac{1}{R_1}[/tex]

[tex]dr={R_1}du[/tex]

So substituting

[tex]\int_R^{R_1} \sqrt{\frac{R_1}{r}-1} dr = R_1\int_R^{R_1}\sqrt{\frac{1}{u}-1} du[/tex]

I can see that if I divide both limits by the factor outside the integral, [itex] R_1[/itex], I'll get the right answer, but surely I can't just do that.

Any hints?

Cheers

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# Homework Help: Simple maths stuff

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