∫0aa2−x2dx=π4a2 \int_{0}^{a} \sqrt[]{a^2-x^2}dx=\frac{\pi }{4}a^2∫0aa2−x2dx=4πa2
∫0a2ax−x2dx=∫0aa2−(x−a)2d(x−a)=π4a2 \int_{0}^{a} \sqrt[]{2ax-x^2}dx= \int_{0}^{a} \sqrt[]{a^2-(x-a)^2}d(x-a)=\frac{\pi }{4}a^2∫0a2ax−x2dx=∫0aa2−(x−a)2d(x−a)=4πa2