第十三單元 旋轉體的體積-剝殼法
Example Let R be the regions bounded by the graphs of and Compute the volume of the solid formed by revolving R about y-axis
Revolving about y-axis
The Method of Shells
Cutting the shell by a scissors
Flattened shell
We have a thin rectangular sheet
Revolving about x-axis
Revolving about x-axis (animate)
The Solid generated by revolving about x-axis
Cutting the shell by a scissors
Opening it up to form a rectangle sheet
Example Let R be the regions bounded by the graphs of and Compute the volume of the solid formed by revolving R about y-axis
Example(continued)
Example Let R be the regions bounded by the graphs of and Compute the volume of the solid formed by revolving R about x-axis
Example(continued)
單元結語 剝殼法對於比較複雜的圖形，有時計算反而要比圓盤法簡單，因為中空圖形剝殼法不必考慮挖洞。 任何旋轉體圖形都可以考慮用圓盤或剝殼法，建議初學者兩種方法都做做看， 當然! 解法正確的話， 答案一定會相同。