Complex numbers use to solve the definite integral | Статья в журнале «Молодой ученый»

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Автор:

Рубрика: Математика

Опубликовано в Молодой учёный №41 (175) октябрь 2017 г.

Дата публикации: 11.10.2017

Статья просмотрена: 22 раза

Библиографическое описание:

Арзиева, С. И. Complex numbers use to solve the definite integral / С. И. Арзиева. — Текст : непосредственный // Молодой ученый. — 2017. — № 41 (175). — С. 1-4. — URL: https://moluch.ru/archive/175/45881/ (дата обращения: 05.03.2021).



These article composite integrals to account we can use at complex numbers. It helps to solve voluntary composite kind of integrals. Complex numbers advantage for technics branches: electric energetic, geology, engineering geology and others.

Keywords: integral, complex number, binomial differential, function

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At this article, we say about to solve nonspecific integral at the method of complex number.

According to binomial differential:

, . [1, p 93]

So,

variable.

In this place,

Just at present, we need to find beneath integral:

and

So, advantage above:

We have found of -1 complex roots: [2, p 186]

These roots of equation equal below:

, , , .

It means that at ,

, .

Below we have found from this formula:

is odd function. So

We use from this formula as a result of:

So, we do to exchange, that is:

If we put in border:

Reply:

Through complex numbers to work a few difficult, but mean this method helps to solve other integrals.

References:

  1. G. N. Berman. “Problems of mathematical analysis”. Moscow 1985.
  2. Yo.U.Soatov. “Higher mathematics” part-2. Tashkent. “Teacher” 1994.


Ключевые слова

integral, complex number, binomial differential, function
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