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Консультация № 184514
Обсуждение
Неизвестный
21.11.2011, 18:00
общий
21.11.2011, 20:25
это ответ
Здравствуйте, Влад Алексеев!
Уточнение:
там конечно V фигуры, а не S должна быть первая буква
и интегралы берутся из того что выражаются функции x(y) и составляются по формуле площади круга pi*x(y)*x(y)
Уточнение:
там конечно V фигуры, а не S должна быть первая буква
и интегралы берутся из того что выражаются функции x(y) и составляются по формуле площади круга pi*x(y)*x(y)
Неизвестный
21.11.2011, 18:16
общий
Уточнение:
там конечно V фигуры, а не S должна быть первая буква
и интегралы берутся из того что выражаются функции x(y) и составляются по формуле площади круга pi*x(y)*x(y)
там конечно V фигуры, а не S должна быть первая буква
и интегралы берутся из того что выражаются функции x(y) и составляются по формуле площади круга pi*x(y)*x(y)
21.11.2011, 20:17
общий
это ответ
Здравствуйте, Влад Алексеев!
Вычислить объём тела, образованного вращением вокруг оси Oy фигуры, ограниченной параболами y = 2 - x[sup]2[/sup] и y = x[sup]2[/sup].
Рассматривая уравнения заданных кривых, видим, что фигура, объём которой необходимо вычислить, симметрична относительно плоскости y = 1. Поэтому достаточно вычислить объём фигуры, образованной вращением параболы y = x2 вокруг заданной оси, и удвоить полученный результат. Выполним указанные действия. Имеем y = x2, x2(y) = y, c = 0, d = 1,
V = 2п [$183$] c[$8747$]dx2dy = 2п [$183$] 0[$8747$]1ydy = 2п [$183$] (y2/2)|01 = пy2|01 = п(1 - 0) = п.
Всё-таки легче вычислить один интеграл, чем два.
С уважением.
Вычислить объём тела, образованного вращением вокруг оси Oy фигуры, ограниченной параболами y = 2 - x[sup]2[/sup] и y = x[sup]2[/sup].
Рассматривая уравнения заданных кривых, видим, что фигура, объём которой необходимо вычислить, симметрична относительно плоскости y = 1. Поэтому достаточно вычислить объём фигуры, образованной вращением параболы y = x2 вокруг заданной оси, и удвоить полученный результат. Выполним указанные действия. Имеем y = x2, x2(y) = y, c = 0, d = 1,
V = 2п [$183$] c[$8747$]dx2dy = 2п [$183$] 0[$8747$]1ydy = 2п [$183$] (y2/2)|01 = пy2|01 = п(1 - 0) = п.
Всё-таки легче вычислить один интеграл, чем два.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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