數值積分
作者:王一哲
日期:2018/1/30
本次課程檔案已上傳至 GeoGebraTube,可以線上操作或下載檔案,網址為 https://ggbm.at/GmAr3WFC
GeoGebra 有內建指令可以畫出數值積分的圖,只要一行就解決了。以下的圖都是以
為例,積分上、下限分別為2、-2,分割數量為20。
長方形法
指令1:RectangleSum
其中長方形對齊點的數值為 0 ~ 1,0代表對齊函數左側,1代表對齊函數右側,0.5代表對齊函數中點。執行指令之後會畫出圖形並顯示計算結果。
Image Not Showing
Possible Reasons
- The image file may be corrupted
- The server hosting the image is unavailable
- The image path is incorrect
- The image format is not supported
Learn More →
RectangleSum(f, -2, 2, 20, 0.5)
Image Not Showing
Possible Reasons
- The image file may be corrupted
- The server hosting the image is unavailable
- The image path is incorrect
- The image format is not supported
Learn More →
RectangleSum(f, -2, 2, 20, 0)
Image Not Showing
Possible Reasons
- The image file may be corrupted
- The server hosting the image is unavailable
- The image path is incorrect
- The image format is not supported
Learn More →
RectangleSum(f, -2, 2, 20, 1)
指令2:LeftSum
以函數左側的數值為長方形對齊點,效果與
相同。
Image Not Showing
Possible Reasons
- The image file may be corrupted
- The server hosting the image is unavailable
- The image path is incorrect
- The image format is not supported
Learn More →
LeftSum(f, -2, 2, 20)
指令3:LowerSum
以函數下方的數值為長方形對齊點。
Image Not Showing
Possible Reasons
- The image file may be corrupted
- The server hosting the image is unavailable
- The image path is incorrect
- The image format is not supported
Learn More →
LowerSum(f, -2, 2, 20)
指令4:UpperSum
以函數上方的數值為長方形對齊點。
Image Not Showing
Possible Reasons
- The image file may be corrupted
- The server hosting the image is unavailable
- The image path is incorrect
- The image format is not supported
Learn More →
UpperSum(f, -2, 2, 20)
梯形法
指令格式如下
執行指令之後會畫出圖形並顯示計算結果。
Image Not Showing
Possible Reasons
- The image file may be corrupted
- The server hosting the image is unavailable
- The image path is incorrect
- The image format is not supported
Learn More →
TrapezoidalSum(f, -2, 2, 20)
積分
其實 GeoGebra 有內建積分指令,有以下4種寫法。
指令1
執行指令之後會計算該函數的積分結果並顯示圖形。
Image Not Showing
Possible Reasons
- The image file may be corrupted
- The server hosting the image is unavailable
- The image path is incorrect
- The image format is not supported
Learn More →
Integral(f)
指令2
對指定的變數積分,其餘變數視為常數。
指令3
將積分的部分標示出來,計算定積分值並顯示計算結果。
Image Not Showing
Possible Reasons
- The image file may be corrupted
- The server hosting the image is unavailable
- The image path is incorrect
- The image format is not supported
Learn More →
Integral(f, -2, 2)
指令4
當布林值為 true 時與指令3功能相同,當布林值為 false 時不顯示計算結果。
Image Not Showing
Possible Reasons
- The image file may be corrupted
- The server hosting the image is unavailable
- The image path is incorrect
- The image format is not supported
Learn More →
Integral(f, -2, 2, false)
參考資料
- 羅驥韡(2013)。GeoGebra幾何與代數的美麗邂逅。臺北市:五南。
- GeoGebra手冊。2018年1月30日,取自 https://wiki.geogebra.org/en/Manual