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

f(x)=x2+sin(2πx)
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

RectangleSum(函數名稱, 積分下限, 積分上限, 長方形數量, 長方形對齊點)

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。

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RectangleSum(f, -2, 2, 20, 0.5)

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RectangleSum(f, -2, 2, 20, 0)

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RectangleSum(f, -2, 2, 20, 1)

指令2:LeftSum

LeftSum(函數名稱, 積分下限, 積分上限, 長方形數量)

以函數左側的數值為長方形對齊點,效果與

RectangleSum(函數名稱, 積分下限, 積分上限, 長方形數量, 0)

相同。

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LeftSum(f, -2, 2, 20)

指令3:LowerSum

LowerSum(函數名稱, 積分下限, 積分上限, 長方形數量)

以函數下方的數值為長方形對齊點。

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LowerSum(f, -2, 2, 20)

指令4:UpperSum

UpperSum(函數名稱, 積分下限, 積分上限, 長方形數量)

以函數上方的數值為長方形對齊點。

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UpperSum(f, -2, 2, 20)

梯形法

指令格式如下

TrapezoidalSum(函數名稱, 積分下限, 積分上限, 梯形數量)

執行指令之後會畫出圖形並顯示計算結果。

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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

Integral(函數名稱)

執行指令之後會計算該函數的積分結果並顯示圖形。

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Integral(f)

指令2

Integral(函數名稱, 變數名稱)

對指定的變數積分,其餘變數視為常數。

指令3

Integral(函數名稱, 積分下限, 積分上限)

將積分的部分標示出來,計算定積分值並顯示計算結果。

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Integral(f, -2, 2)

指令4

Integral(函數名稱, 積分下限, 積分上限, 布林值)

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。

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Integral(f, -2, 2, false)

參考資料

  1. 羅驥韡(2013)。GeoGebra幾何與代數的美麗邂逅。臺北市:五南。
  2. GeoGebra手冊。2018年1月30日,取自 https://wiki.geogebra.org/en/Manual


tags:GeoGebra