第十一單元 兩曲線圍出的面積
Area
Area of a Region Bounded by Two Graphs
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
Example
Example
Area Between Two Curves Formula
Making Sure Which Curve is on Top
Example Solution: (1)Sketching the graphs of both function
(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 Example(continued) (3)Slice it into thin pieces, pretending it is a rectangle
Example(continued) (4) Add up and take the limit as the piece width tend to zero (Integrate)
Area of a Region Bounded by Two Graphs (Horizontal Strips)
Area Between Two Curves Formula
Example Solution: (1)Sketching the graphs of both function
(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
Example(continued) (4) Add up and take the limit as the piece width tend to zero (Integrate)
Example
Vetical or Horizontal Strips
Example(continued)
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。