Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Please help to calculate: $$\int\sqrt {{r}^{2}-{x}^{2}}{dx},\quad x\in[0,r]$$ Do any method of trigonometric substitution?


share|cite|improve this question
up vote 5 down vote accepted

Use the substitution $x=r\sin t$.

share|cite|improve this answer
Good!. Thanks so much! – mathsalomon Aug 25 '11 at 23:37
@mathsalomon: You are welcome! – Américo Tavares Aug 25 '11 at 23:41
For future reference. That difference of squares may remind you of a certain right triangle. Use it to find a good substitution to use. – GEdgar Aug 26 '11 at 0:26

Or use the substitution x = r cosh t if you like calculus on the complex plane.

share|cite|improve this answer
Hadamard said, "Le plus court chemin entre deux vérités dans le domaine réel passe par le domaine complexe." This is an example where that quote is not apropos. – Jonas Meyer Aug 26 '11 at 0:42

Your Answer


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.