題目 Problem (D). Rotate the region {(x,y):0≤x≤π and 0≤y≤sinx}\{(x,y):0\le x\le \pi \text{ and } 0\le y\le \sin x\}{(x,y):0≤x≤π and 0≤y≤sinx} about the xxx-axis. Find the volume of the solid obtained. Answer. (5)‾\underline{\quad(5)\quad}(5). 解答 解法一 思路 展開 繞 xxx 軸以圓盤法累加半徑 sinx\sin xsinx 的截面。 答題過程 展開 V=π∫0πsin2x dx=π⋅π2=π22.V=\pi\int_0^\pi\sin^2x\,\mathrm{d}x =\pi\cdot\frac\pi2 =\boxed{\frac{\pi^2}{2}}.V=π∫0πsin2xdx=π⋅2π=2π2.
