第十一單元 兩曲線圍出的面積.

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1 第十一單元 兩曲線圍出的面積

2 Area

3 Area of a Region Bounded by Two Graphs

4 Area of a Region Bounded by Two Graphs (Vetical Strips)
If f and g are continuous on [a,b] and f (x) ≥ g(x), then

5 Example

6 Example

7 Area Between Two Curves
Formula

8 Making Sure Which Curve is on Top

9 Example Solution: (1)Sketching the graphs of both function

10 (2) To find the points of intersection of the two graphs
Example(continued) (2) To find the points of intersection of the two graphs

11 (3)Slice it into thin pieces, pretending it is a rectangle
Example(continued) (3)Slice it into thin pieces, pretending it is a rectangle

12 Example(continued) (4) Add up and take the limit as the piece width tend to zero (Integrate)

13 Area of a Region Bounded by Two Graphs (Horizontal Strips)

14 Area Between Two Curves
Formula

15 Example Solution: (1)Sketching the graphs of both function

16 (2) To find the points of intersection of the two graphs
Example(continued) (2) To find the points of intersection of the two graphs (3)Slice it into thin pieces, pretending it is a rectangle

17 Example(continued) (4) Add up and take the limit as the piece width tend to zero (Integrate)

18 Example

19 Vetical or Horizontal Strips

20 Example(continued)

21 單元結語 同學遇到需要計算面積的題型時，常常希望將公式代入就計算出答案，這種作法是非常容易發生錯誤的，因為少了畫圖這個步驟，高低無法判斷，造成正負相抵而得到錯誤的答案。 對於各類型的函數應多加練習函數的繪圖與積分的技巧。