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Консультация № 192065
09.12.2017, 14:42
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
Вычислить объем тела, ограниченного поверхностями:
Приложение:
Вычислить объем тела, ограниченного поверхностями:
Приложение:
Прикрепленные файлы:
Обсуждение
09.12.2017, 14:57
общий
Адресаты:
Сообщите, пожалуйста, для экспертов, каковы Ваши соображения по решению этой задачи, если они есть. Возможно, будет, что обсудить.
Об авторе:
Facta loquuntur.
Facta loquuntur.
10.12.2017, 11:07
общий
Адресаты:
Сначала нужно разобраться, что собой представляет заданное тело. Для этого Вам придётся выполнить рисунок.
Об авторе:
Facta loquuntur.
Facta loquuntur.
19.12.2017, 14:43
общий
это ответ
Здравствуйте, natashak2001!
Объем тела вычисляется с помощью тройного интеграла:
В данном случае тело ограничено снизу плоскостью z = 0, сверху - плоскостью z = y+1 (причём y+1 > 0 при y > -1), сбоку - плоскостью y = 9x и поверхностью y = x[sup]3[/sup]. Две последние поверхности пересекаются при x = y = 0 и при x = 3, y =27, причём при 0 < x < 3 имеем 3x > x[sup]3[/sup]. Следовательно, при переходе от тройного интеграла к повторному пределы интегрирования будут следующими: x от 0 до 3, y от x[sup]3[/sup] до 9x и z от 0 до y+1, то есть
Объем тела вычисляется с помощью тройного интеграла:
В данном случае тело ограничено снизу плоскостью z = 0, сверху - плоскостью z = y+1 (причём y+1 > 0 при y > -1), сбоку - плоскостью y = 9x и поверхностью y = x[sup]3[/sup]. Две последние поверхности пересекаются при x = y = 0 и при x = 3, y =27, причём при 0 < x < 3 имеем 3x > x[sup]3[/sup]. Следовательно, при переходе от тройного интеграла к повторному пределы интегрирования будут следующими: x от 0 до 3, y от x[sup]3[/sup] до 9x и z от 0 до y+1, то есть
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Спасибо за помощь!
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