3-ta’rif. Agar da (r) funksiyaning limiti mavjud bo‘lsa, bu limit f(x) funksiyaning oraliqdagi xosmas integrali deb ataladi va u kabi belgilanadi. Demak,
(2)
4-ta’rif. Agar da (r) funksiyaning limiti mavjud bo‘lib, u chekli bo‘lsa, (2) xosmas integral yaqinlashuvchi deyiladi, f(x) esa cheksiz oraliqda integrallanuvchi funksiya deb ataladi.
Agar da (r) ning limiti cheksiz bo‘lsa yoki mavjud bo‘lmasa, (2) integral uzoqlashuvchi deyiladi.
3-misol. ni yaqinlashishga tekshiring.
Yechish. Bu xosmas integral uzoqlashuvchi bo‘ladi, chunki da
![](data:image/png;base64,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)
funksiya limitga ega emas.
4-misol. ni yaqinlashishga tekshiring.
Yechish. .
Demak, integral yaqinlashuvchi va
.
Aytaylik, f(x) funksiya (-;+) da uzluksiz bo‘lsin. U holda biror c(-;+) uchun va integrallar yig‘indisi bu funksiyaning ikkala integrallash chegaralari ham cheksiz bo‘lgan xosmas integrali deyiladi va quyidagicha yoziladi: . Demak,
= +
va ta’rif bo‘yicha
= + (3)
deb qabul qilamiz.
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