Ichikquriq

Katsun hukllata wataq f(x) sharishqa wichqashqa patma kaypuchaw I = [a, b] . Kutsushun I-ta $x_{i}==a+{\frac {b-a}{n}}\,\ i=0,1,...,n$ aqukunawan n kaypu pakiman, kayanqa patsallan sutayniyuq. Llapan kaypu pakichaw $[x_{i-1},x_{i}]\,\ i=1,...,n,$, akrakan llutay llutaa huk aquta $\xi _{i}$ , kaynawta $\xi _{i}\in [x_{i-1},x_{i}]$.

Tsaypitaqa kay yapaskishqata $f(\xi _{1})\Delta x_{1}+...+f(\xi _{n})\Delta x_{n}=\sum _{i=1}^{n}f(\xi _{i})\Delta x_{i}$ tsaychaw $\Delta x_{i}=x_{i}-x_{i-1}$, shutitsantsik f hukllata wataqpa yapaskishqa huñuqnin .

Kay harkana : $\lim _{n\to \infty }\sum _{i=1}^{n}f(\xi _{i})\Delta x_{i}$ kaptin, mana aqu akray ashipaptin $\xi _{i}$, kay hukllata wataqta nintsik [a; b] wichqashqa patma kaypuchaw huñupalla. Harkanata nintsik hukllata wataqpa ichikquriqnin [a; b] wichqashqa patma kaypuchaw. Qillqarintsik kaynaw

$\int _{a}^{b}f(x)\,{\text{d}}x$

.