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第十二單元

第十二單元. 旋轉體的體積 - 圓盤法. Volumes of a Solid. The volumes of solid that can be cut into thin slices, where the volumes can be interpreted as a definite integral. Slicing the solid into thin slabs. The formula of volume of Solid.

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第十二單元

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  1. 第十二單元 旋轉體的體積-圓盤法

  2. Volumes of a Solid • The volumes of solid that can be cut into thin slices, where the volumes can be interpreted as a definite integral.

  3. Slicing the solid into thin slabs

  4. The formula of volume of Solid • The volume V of the solid should be given approximately by the Riemann sum

  5. Solids of Revolution • 1. The Method of Disks • 2. The Method of Shells

  6. 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

  7. Revolving about y-axis

  8. The Method of Disks

  9. The Method of Disks(2)

  10. Revolving about x-axis

  11. Revolving about x-axis (animate)

  12. The Solid by revolving about x-axis

  13. The Solid by revolving about x-axis

  14. 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

  15. Example(continued)

  16. 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

  17. Example(continued)

  18. 單元結語 • 求旋轉體的體積不要死背公式，要用分割切薄片的觀念解題，公式只要遇到變化的狀況就無效了。 • 一般來說，對付簡單的題型，圓盤法計算及觀念較簡單，適宜初學者使用

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