題目 4. (15%)(15\%)(15%) Find the volume of the ellipsoid generated by resolving the semiellipse y=1aa2−x2, ∣x∣≤a,y=\frac{1}{a}\sqrt{a^2-x^2},\ |x|\le a,y=a1a2−x2, ∣x∣≤a, about the xxx-axis. 解答 解法一 答題過程 展開 圓盤旋轉法給 V=π∫−aaa2−x2a2 dx=4πa3.V=\pi\int_{-a}^{a}\frac{a^2-x^2}{a^2}\,\mathrm{d}x=\boxed{\frac{4\pi a}{3}}.V=π∫−aaa2a2−x2dx=34πa.
