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

Thanks.

2 Answers 2

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

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    For future reference. That difference of squares may remind you of a certain right triangle. Use it to find a good substitution to use.2011-08-26
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Or use the substitution x = r cosh t if you like calculus on the complex plane.

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    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.2011-08-26