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Консультация № 201537
23.10.2021, 14:58
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Здравствуйте! Прошу помощи в следующем вопросе:
Помогите, пожалуйста, найти площади фигур, ограниченных данными линиями.
Помогите, пожалуйста, найти площади фигур, ограниченных данными линиями.
Обсуждение
23.10.2021, 17:12
общий
Адресаты:
Достаточно начертить графики, и картина проясняется, "как на ладони".
Выделяем полные квадраты из первых 2х квадратичных уравнений:
y^2 - 4*y + x^2 = 0 ==> (y^2 - 2*2*y + 4) - 4 + x^2 = 0 ==> (y-2)^2 + x^2 = 2^2 это окружность радиуса 2 с центром в тчк O1(0 ; 2).
y^2 - 6*y + x^2 = 0 ==> (y^2 - 2*3*y + 9) - 9 + x^2 = 0 ==> (y-3)^2 + x^2 = 3^2 это окружность радиуса 3 с центром в тчк O2(0 ; 3).
Площадь фигуры, ограниченной данными линиями отмечена мною голубой заливкой на ниже-приложенном графике.
Дальше сами сможете подсчитаеть площадь?
Выделяем полные квадраты из первых 2х квадратичных уравнений:
y^2 - 4*y + x^2 = 0 ==> (y^2 - 2*2*y + 4) - 4 + x^2 = 0 ==> (y-2)^2 + x^2 = 2^2 это окружность радиуса 2 с центром в тчк O1(0 ; 2).
y^2 - 6*y + x^2 = 0 ==> (y^2 - 2*3*y + 9) - 9 + x^2 = 0 ==> (y-3)^2 + x^2 = 3^2 это окружность радиуса 3 с центром в тчк O2(0 ; 3).
Площадь фигуры, ограниченной данными линиями отмечена мною голубой заливкой на ниже-приложенном графике.
Дальше сами сможете подсчитаеть площадь?
25.10.2021, 02:40
общий
Адресаты:
Вы отсутствуете на странице своей Консультации уже 1,5 суток, вероятно Вы уже забросили её и в помощи не нуждаетесь.
Тогда и мне тут нЕчего делать.
Когда и если Вы сюда вернётесь, почитайте учебную статью по Вашей теме "Как вычислить площадь фигуры в полярных координатах с помощью интеграла?" Ссылка
Тогда и мне тут нЕчего делать.
Когда и если Вы сюда вернётесь, почитайте учебную статью по Вашей теме "Как вычислить площадь фигуры в полярных координатах с помощью интеграла?" Ссылка
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