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Консультация № 201165
15.06.2021, 13:17
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Вычислить двойной интеграл по области , ограниченной указанными линиями.
Вычислить двойной интеграл по области , ограниченной указанными линиями.
Прикрепленные файлы:
Обсуждение
15.06.2021, 22:42
общий
это ответ
Здравствуйте, Salton!
Чтобы получить наглядное представление об области интегрирования
вычислим координаты точек пересечения заданных линий. Из уравнения первой линии получим, что 
а из уравнения второй линии -- что 
Тогда
Значит, заданные линии пересекаются в точках
Область график которой построен с применением онлайн-калькулятора, показана на рисунке в прикреплённом файле окрашенной в серый цвет.
Вычислим заданный интеграл:
(решение смотрите здесь: Ссылка >>);
(решение смотрите здесь: Ссылка >>);
(решение смотрите здесь: Ссылка >>);
Однако, такое решение оказалось весьма трудоёмким. Лучше поступить так:
Чтобы получить наглядное представление об области интегрирования
вычислим координаты точек пересечения заданных линий. Из уравнения первой линии получим, что а из уравнения второй линии -- что ТогдаЗначит, заданные линии пересекаются в точках
Область
график которой построен с применением онлайн-калькулятора, показана на рисунке в прикреплённом файле окрашенной в серый цвет.Вычислим заданный интеграл:
(решение смотрите здесь: Ссылка >>); (решение смотрите здесь: Ссылка >>); (решение смотрите здесь: Ссылка >>);
(решение смотрите здесь: 
Однако, такое решение оказалось весьма трудоёмким. Лучше поступить так:
Прикрепленные файлы:
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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