定積分

定義 5.9 (定積分)   区間 $a\leq x \leq b$ を

$$a=x_{0}<x_{1}<x_{2}<\cdots<x_{k-1}<x_{k}<\cdots<x_{n-1}<x_{n}=b$$ (711)

と分割する．

$$\int_{a}^{b}f(x)\,dx= \lim_{n\to\infty}\sum_{k=1}^{n}f(\xi_{k})\Delta x_{k}$$ (712)

$$\xi_{k}\in I_{k}=\{x_{k}\leq x\leq x_{k-1}\}$$ (713)

$$\Delta x_{k}=x_{k}-x_{k-1}$$ (714)

Kondo Koichi
Created at 2002/09/12