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Консультация № 201034
01.06.2021, 16:17
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Вычислить тройной интеграл:
Вычислить тройной интеграл:
Прикрепленные файлы:
Обсуждение
03.06.2021, 13:17
общий
Адресаты:
Как использовать Ваши квадрат-корни [$8730$](8 - x2 - y2) ; [$8730$](y2 + x2) , со знаком плюс перед ними, либо [$177$][$8730$](y2 + x2) ?
Устроит ли Вас решение в Маткаде?
Устроит ли Вас решение в Маткаде?
06.06.2021, 09:49
общий
Прошу продлить срок действия консультации на пять дней. Возможно, удастся выбрать время для ответа на вопрос.
Об авторе:
Facta loquuntur.
Facta loquuntur.
06.06.2021, 12:23
общий
Адресаты:
Андрей Владимирович, спасибо... Не сложно, но приятно было выполнить Вашу просьбу для Вас
Об авторе:
С уважением
shvetski
С уважением
shvetski
09.06.2021, 11:13
общий
это ответ
Здравствуйте, lyskov.kirill!
Уравнение
задаёт верхнюю часть сферы, радиус которой равен 
а центр находится в начале координат. Уравнение 
задаёт верхнюю часть конуса второго порядка 
Неравенство 
задаёт плоскость 
и расположенное за ней полупространство 
Выясним, по какой линии пересекаются заданные полусфера и часть конуса второго порядка:
то есть линия пересечения полусферы и части конуса второго порядка -- окружность, которая задаётся уравнениями
Проекция этой окружности на плоскость
задаётся уравнением 
Значит, область
представляет собой фигуру, которая ограничена снизу верхней частью конуса второго порядка 
сверху -- сферой 
спереди -- плоскостью 
Эту фигуру можно задать следующей системой неравенств:
На рисунке в прикреплённом файле указанная фигура показана на фронтальной и горизонтальной проекциях и закрашена серым цветом.
Переходя к цилиндрической системе координат, получим
(интеграл вычислен здесь: Ссылка >>);
Уравнение
задаёт верхнюю часть сферы, радиус которой равен а центр находится в начале координат. Уравнение задаёт верхнюю часть конуса второго порядка Неравенство задаёт плоскость и расположенное за ней полупространство Выясним, по какой линии пересекаются заданные полусфера и часть конуса второго порядка:
то есть линия пересечения полусферы и части конуса второго порядка -- окружность, которая задаётся уравнениями
Проекция этой окружности на плоскость
задаётся уравнением Значит, область
представляет собой фигуру, которая ограничена снизу верхней частью конуса второго порядка сверху -- сферой спереди -- плоскостью Эту фигуру можно задать следующей системой неравенств:На рисунке в прикреплённом файле указанная фигура показана на фронтальной и горизонтальной проекциях и закрашена серым цветом.
Переходя к цилиндрической системе координат, получим
(интеграл вычислен здесь: Ссылка >>);
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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