ThmDex – An index of mathematical definitions, results, and conjectures.
Result R3535 on D168: Pi
Subresult of R3227: Riemann integral of semicircle
Riemann integral of unit semicircle
Formulation 0
Let $\pi$ be the D168: Pi.
Then \begin{equation} \int^1_{-1} \sqrt{1^2 - x^2} \, d x = \frac{1}{2} \pi \end{equation}
Proofs
Proof 0
Let $\pi$ be the D168: Pi.
This result is a particular case of R3227: Riemann integral of semicircle. $\square$