I'm stuck on this step trying to solve a math puzzle. How do I integrate this?
Integrate over $t$ if $dr/dt = \sqrt{1 - r^2}$?
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calculus
integration
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0Please 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
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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). $