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Консультация № 191563
28.10.2017, 09:58
0.00 руб.
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1
1
Здравствуйте, уважаемые эксперты! Помогите, пожалуйста с решением:Вычислить с помощью тройного интеграла объём тела, ограниченного указанными поверхностями. Сделать чертёж данного тела и его проекции на плоскость xOy: z = 0, z = x^2 + y^2, x^2 + y^2 = 4.
Обсуждение
30.10.2017, 15:03
общий
это ответ
Здравствуйте, olja_12111983!
Данное тело ограничено снизу плоскостью
сверху - параболоидом вращения 
с боков - цилиндром 
Рисунок ниже выполнен с помощью программы автоматизированного построения трёхмерных поверхностей.
Проекция тела на плоскость
- круг 
Рассматриваемое тело симметрично относительно плоскостей
и 
Поэтому его объём можно вычислить как учетверённый объём той части тела, которая находится в первом октанте координатного пространства 
Вычислим объём. переходя к цилиндрическим координатам:
(ед. объёма).
Данное тело ограничено снизу плоскостью
сверху - параболоидом вращения с боков - цилиндром Рисунок ниже выполнен с помощью программы автоматизированного построения трёхмерных поверхностей.Проекция тела на плоскость
- круг Рассматриваемое тело симметрично относительно плоскостей
и Поэтому его объём можно вычислить как учетверённый объём той части тела, которая находится в первом октанте координатного пространства Вычислим объём. переходя к цилиндрическим координатам:
(ед. объёма).
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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