Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

share|improve this question
    
you cannot integrate this directly but need to first 'separate the variables' in order to solve the equation. Once you've done that, the integral will be a standard result. –  Ronald Apr 29 '12 at 23:07
    
Stuck on what step? Please make the body of your post self-contained. You don't ask readers of a book to start at the spine; you shouldn't ask readers of your post to start at the subject, which is just an indexing item. –  Arturo Magidin Apr 29 '12 at 23:07
    
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. –  Gerry Myerson Apr 29 '12 at 23:07
add comment

2 Answers

up vote 2 down vote accepted

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 $C$.

share|improve this answer
add comment

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

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.