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Консультация № 195643
17.05.2019, 15:18
0.00 руб.
18.05.2019, 06:29
0
2
1
Здравствуйте! Прошу помощи в следующем вопросе:
Вычислите координаты центра масс однородного тела, занимающего область [b]V[/b], если [b]V: y=x[sup]2[/sup]+z[sup]2[/sup], x[sup]2[/sup]+z[sup]2[/sup]=10, y=0[/b].
Вычислите координаты центра масс однородного тела, занимающего область [b]V[/b], если [b]V: y=x[sup]2[/sup]+z[sup]2[/sup], x[sup]2[/sup]+z[sup]2[/sup]=10, y=0[/b].
Обсуждение
20.05.2019, 08:39
общий
это ответ
Здравствуйте, Apricot!
Уравнение
или 
задаёт эллиптический параболоид; уравнение 
задаёт круговой цилиндр [1, с. 89, 94]. Рассматриваемое тело ограничено снизу кругом 
а сверху -- параболоидом который является результатом вращения параболы 
вокруг оси ординат. В соответствии с формулой (41.7) [1, с. 246] искомый объём как разность объёмов кругового цилиндра с радиусом 
и высотой 
и параболоида, получаемого вращением кривой 
с той же высотой равен
(ед. объёма).
Усложнять решение задачи применением кратных интегралов в данном случае, по-моему, не нужно.
Литература
1. Письменный Д. Т. Конспект лекций по высшей математике. В 2 ч. Ч. 1. -- М.: Айрис-пресс, 2006. -- 288 с.
Уравнение
или задаёт эллиптический параболоид; уравнение задаёт круговой цилиндр [1, с. 89, 94]. Рассматриваемое тело ограничено снизу кругом а сверху -- параболоидом который является результатом вращения параболы вокруг оси ординат. В соответствии с формулой (41.7) [1, с. 246] искомый объём как разность объёмов кругового цилиндра с радиусом и высотой и параболоида, получаемого вращением кривой с той же высотой равен (ед. объёма).Усложнять решение задачи применением кратных интегралов в данном случае, по-моему, не нужно.
Литература
1. Письменный Д. Т. Конспект лекций по высшей математике. В 2 ч. Ч. 1. -- М.: Айрис-пресс, 2006. -- 288 с.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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