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Консультация № 202969
04.06.2022, 00:22
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Здравствуйте! У меня возникли сложности с таким вопросом, помогите, пожалуйста:
Найдите центр тяжести плоской фигуры, ограниченной кривыми: x=1, y=x^3, y=-квадратный корень(x)
Найдите центр тяжести плоской фигуры, ограниченной кривыми: x=1, y=x^3, y=-квадратный корень(x)
Обсуждение
05.06.2022, 04:51
общий
Адресаты:
Начертите свою фигуру на простом плоском графике XOY .
Изучите хорошую учебную статью по Вашей теме "Как вычислить центр тяжести плоской ограниченной фигуры с помощью двойного интеграла?" Ссылка.
Дальше сами справитесь?
Изучите хорошую учебную статью по Вашей теме "Как вычислить центр тяжести плоской ограниченной фигуры с помощью двойного интеграла?" Ссылка.
Дальше сами справитесь?
05.06.2022, 23:50
общий
Адресаты:
Я рад Вашим Успехам!
Спасибо Вам за сообщение и сэкономленное время!
Спасибо Вам за сообщение и сэкономленное время!
06.06.2022, 17:27
общий
это ответ
Здравствуйте, kotb9!
Заданная фигура обозначена на рисунке в прикреплённом файле заливкой серого цвета. Вычислим сначала её площадь:
(ед. площади)
(вычисление интеграла показано здесь: Ссылка >>). Принимая поверхностную плотность равной единице, вычислим её массу:
(ед. массы).
Вычислим статические моменты заданной фигуры, считая поверхностную плотность равной единице:
(ед. статич. момента);
(ед. статич. момента).
Вычислим координаты центра тяжести заданной фигуры.
(ед. длины), 
(ед. длины).
Заданная фигура обозначена на рисунке в прикреплённом файле заливкой серого цвета. Вычислим сначала её площадь:
(ед. площади)(вычисление интеграла показано здесь: Ссылка >>). Принимая поверхностную плотность равной единице, вычислим её массу:
(ед. массы).Вычислим статические моменты заданной фигуры, считая поверхностную плотность равной единице:
(ед. статич. момента); (ед. статич. момента).Вычислим координаты центра тяжести заданной фигуры.
(ед. длины), (ед. длины).
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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