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Консультация № 201120
08.06.2021, 11:51
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
вычислить объем тела, ограниченного поверхностями:
вычислить объем тела, ограниченного поверхностями:
Прикрепленные файлы:
Обсуждение
09.06.2021, 02:52
общий
это ответ
Объем тела вычисляется с помощью тройного интеграла:
В данном случае тело ограничено снизу плоскостью z = 0, сверху - плоскостью z = y при y > 0, сбоку - параболическим цилиндром y = 4-x[sup]2[/sup], пересекающимся с плоскостью y = 0 при x = [$177$]2. Следовательно, при переходе от тройного интеграла к повторному пределы интегрирования будут следующими: x от -2 до 2, y от 0 до 4-x[sup]2[/sup] и z от 0 до y, то есть
В данном случае тело ограничено снизу плоскостью z = 0, сверху - плоскостью z = y при y > 0, сбоку - параболическим цилиндром y = 4-x[sup]2[/sup], пересекающимся с плоскостью y = 0 при x = [$177$]2. Следовательно, при переходе от тройного интеграла к повторному пределы интегрирования будут следующими: x от -2 до 2, y от 0 до 4-x[sup]2[/sup] и z от 0 до y, то есть
(ед. объёма).
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