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I'm stuck on this step trying to solve a math puzzle. How do I integrate this?

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    Please include the question in the question, not just in the title. In any event, it is not clear exactly what integral you are trying to evaluate.2012-04-29

2 Answers 2

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You have that

$\frac{{dr}}{{dt}} = \sqrt {1 - {r^2}} $

from where

$\frac{{dr}}{{\sqrt {1 - {r^2}} }} = dt$

then integrating

$\arcsin r + C = t$

You need a initital value to determine $C$.

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I think you are asking to solve a differential equation. This one is separable, so one has $ \arcsin(r) = t + C $ or $ r = \sin(t + C). $