第十三單元 旋轉體的體積-剝殼法.

Presentation on theme: "第十三單元 旋轉體的體積-剝殼法."— Presentation transcript:

1 第十三單元 旋轉體的體積-剝殼法

2 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

3 Revolving about y-axis

4 The Method of Shells

5 Cutting the shell by a scissors

6 Flattened shell

7 We have a thin rectangular sheet

8 Revolving about x-axis

9 Revolving about x-axis (animate)

10 The Solid generated by revolving about x-axis

11 Cutting the shell by a scissors

12 Opening it up to form a rectangle sheet

13 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

14 Example(continued)

15 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

16 Example(continued)

17 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。