http://10.8.1.3/class/ 2026-05-09T20:58:53+00:00 http://10.8.1.3/class/ http://10.8.1.3/class/lib/exe/fetch.php?media=wiki:dokuwiki.svg text/html 2026-05-01T03:54:40+00:00 yuki (yuki@undisclosed.example.com) http://10.8.1.3/class/doku.php?id=numericalipa:lecture3&rev=1777607680&do=diff 【数値情報処理a】第3回 数値積分 前回の課題 【数値情報処理a】第2回の答え 積分 $x$ の区間 $[a,b]$ で関数 $y=f(x)$ と $x$ 軸ではさまれた領域の面積 $S$ は積分（定積分）で求められる。 \[ S=\int_{a}^{b}f(x)dx=[F(x)]_{a}^{b}=F(b)-F(a) \] $x$ を積分変数、 $f(x)$ を被積分関数、 $F(x)$ を $f(x)$ の原始関数$F(x)$$x$$f(x)$\[ \frac{dF(x)}{dx}=F^{\prime}(x)=f(x) \]$f(x)$$F(x)$$f(x)$$F(x)$$[a,b]$\[ f(x)=x^{n}\quad(n\neq -1) \]$f(x)$\[ F(x)=\frac{1}{n+1}x^{n+1} \]\[ S=\int_{a}^{b}x^{n}dx=\left[\frac{1}{n+1}x^{n+1}\right]_{a}^{b}=\frac{b^{n+1}-a^{n+1}}{n+1} \]$n=1$\[ f(x)=x \]\[ S=\int_{a}^{b}… text/html 2026-04-29T15:28:02+00:00 yuki (yuki@undisclosed.example.com) 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