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Консультация № 201523
19.10.2021, 19:12
0.00 руб.
0
7
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос: вычислить интеграл sinx/x от 0 до бесконечности через е^(-лямда х) на синус х, дх. очень нужен именно этот способ. заранее спасибо
Обсуждение
19.10.2021, 19:52
общий
Адресаты:
Мне самому стало интересно, смогут ли оставшиеся на портале знатоки математики осилить выражение интегрального синуса через указанную Вами функцию. Это как смотреть по телевизору триллер с неизвестным финалом. Браво! 
Об авторе:
Facta loquuntur.
Facta loquuntur.
19.10.2021, 20:44
общий
такой вот преподаватель: то интеграл поверхностный одним ему известным способом задаст, то неведомые методы требует. грустно, но деваться некуда
19.10.2021, 20:59
общий
Адресаты:
Я сочувствую Вам. Однако при более внятной формулировке задания с поверхностным интегралом с ним мог бы разобраться даже я, отнюдь не знаток математики. А здесь речь идёт о специальных функциях. Вы их изучали?
Вам для информации: Ссылка >> (я не склонен ссылаться на Википедию, но в данном случае сделал исключение из правила).
Вам для информации: Ссылка >> (я не склонен ссылаться на Википедию, но в данном случае сделал исключение из правила).
Об авторе:
Facta loquuntur.
Facta loquuntur.
19.10.2021, 23:23
общий
интегральный синус. его и надо разложить подробно. изучение происходит самостоятельно, т.к. был перевод из одного вуза в другой, требуется досдать недостающий материал
20.10.2021, 04:42
общий
Адресаты:
Значит, Вы получаете повышенную математическую подготовку. У меня, например, её нет. Поэтому рассматриваемое задание для меня непосильно. 
Об авторе:
Facta loquuntur.
Facta loquuntur.
22.10.2021, 15:55
общий
23.10.2021, 13:19
это ответ
Рассмотрим такой интеграл (считая x постоянным параметром):
Тогда
и
(здесь мы изменили порядок интегрирования). Внутренний интеграл вычисляется интегрированием по частям:
откуда
и
Соответственно,
что соответствует известному свойству интегрального синуса:
Тогда
и
(здесь мы изменили порядок интегрирования). Внутренний интеграл вычисляется интегрированием по частям:
откуда
и
Соответственно,
что соответствует известному свойству интегрального синуса:
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