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Консультация № 195881
21.06.2019, 02:02
0.00 руб.
22.06.2019, 19:18
1
2
2
Здравствуйте! У меня возникли сложности с таким вопросом:
12. Вычислить объём тела вращения вокруг оси OY фигуры, ограниченной графиками функций y = x[sup]2[/sup], y = 0, x = 2.
12. Вычислить объём тела вращения вокруг оси OY фигуры, ограниченной графиками функций y = x[sup]2[/sup], y = 0, x = 2.
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Обсуждение
25.06.2019, 12:15
общий
это ответ
Здравствуйте, naks1mok!
В общем случае объем тела вращения вокруг оси OY определяется по формуле:
если фигура ограничена кривыми x[sub]1[/sub](y), x[sub]2[/sub](y) и прямыми y = y[sub]1[/sub], y = y[sub]2[/sub] (причём x[sub]1[/sub](y) < x[sub]2[/sub](y) при y[sub]1[/sub] < y < y[sub]2[/sub]).
В данном случае имеем x[sub]1[/sub](y) = [$8730$]y (функция, обратная y = x[sup]2[/sup]), x[sub]2[/sub](y) = 2, y[sub]1[/sub] = 0, y[sub]2[/sub] = 4 (точка пересечения кривой y=x[sup]2[/sup] и прямой x=2), поэтому объем тела вращения будет равен
В общем случае объем тела вращения вокруг оси OY определяется по формуле:
если фигура ограничена кривыми x[sub]1[/sub](y), x[sub]2[/sub](y) и прямыми y = y[sub]1[/sub], y = y[sub]2[/sub] (причём x[sub]1[/sub](y) < x[sub]2[/sub](y) при y[sub]1[/sub] < y < y[sub]2[/sub]).
В данном случае имеем x[sub]1[/sub](y) = [$8730$]y (функция, обратная y = x[sup]2[/sup]), x[sub]2[/sub](y) = 2, y[sub]1[/sub] = 0, y[sub]2[/sub] = 4 (точка пересечения кривой y=x[sup]2[/sup] и прямой x=2), поэтому объем тела вращения будет равен
25.06.2019, 14:50
общий
это ответ
Здравствуйте, naks1mok!
Искомый объём вычислим как разность между объёмами кругового цилиндра, получаемого вращением отрезка прямой
и параболоида, получаемого вращением параболы 
ограниченных прямыми 
и 
вокруг оси 
По формуле (41.8) [1, с. 247] получим
(ед. объёма).
Литература
1. Письменный Д. Т. Конспект лекций по высшей математике: в 2 ч. Ч. 1. -- М.: Айрис-пресс, 2007. -- 288 с.
Искомый объём вычислим как разность между объёмами кругового цилиндра, получаемого вращением отрезка прямой
и параболоида, получаемого вращением параболы ограниченных прямыми и вокруг оси По формуле (41.8) [1, с. 247] получим (ед. объёма).Литература
1. Письменный Д. Т. Конспект лекций по высшей математике: в 2 ч. Ч. 1. -- М.: Айрис-пресс, 2007. -- 288 с.
5
Спасибо!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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