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Консультация № 197069
13.11.2019, 18:37
0.00 руб.
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1
Здравствуйте,
Найти площадь фигуры,
ограниченной линиями
y = x/2 , y = x/8 , y = 9
Найти площадь фигуры,
ограниченной линиями
y = x/2 , y = x/8 , y = 9
Обсуждение
19.11.2019, 13:52
общий
Адресаты:
Я к mustang289 : Я ответил на 3 Ваши Вопроса rfpro.ru/question/195521 от 6мая2019 , rfpro.ru/question/195520 , rfpro.ru/question/195519 , потратил много часов на подготовку и проверку правильности своих ответов.
От Вас не возвратилось ни Оценки за Ответы , ни Спасибо за старания. Эксперты утрачивают активность и перестают отвечать на вопросы изза таких неблагодарных авторов вопросов. Стараться для Вас - всё равно, что тратить свою жизнь в пустоту.
От Вас не возвратилось ни Оценки за Ответы , ни Спасибо за старания. Эксперты утрачивают активность и перестают отвечать на вопросы изза таких неблагодарных авторов вопросов. Стараться для Вас - всё равно, что тратить свою жизнь в пустоту.
23.11.2019, 13:06
общий
это ответ
Здравствуйте, mustang289!
Площадь фигуры, ограниченной графиками линиями y[sub]1[/sub](x) и y[sub]2[/sub](x), вычисляется с помощью двойного интеграла
где y[sub]1[/sub](x) = y[sub]2[/sub](x) при x = x[sub]1[/sub], x = x[sub]2[/sub] и y[sub]1[/sub](x) < y[sub]2[/sub](x) при x[sub]1[/sub] < x < x[sub]2[/sub]. Если уравнения линий можно записать в виде x = x[sub]1[/sub](y) и x = x[sub]2[/sub](y), то интеграл примет вид
где x[sub]1[/sub](y) = x[sub]2[/sub](y) при y = y[sub]1[/sub], y = y[sub]2[/sub] и x[sub]1[/sub](y) < x[sub]2[/sub](y) при y[sub]1[/sub] < y < y[sub]2[/sub].
В данном случае проще использовать второй вариант: x[sub]1[/sub] = 2y, x[sub]2[/sub] = 8y, приравнивая x[sub]1[/sub] = x[sub]2[/sub], получаем
причём при 0 < y < 9 имеем x[sub]1[/sub] < x[sub]2[/sub].
Тогда искомая площадь будет равна
Площадь фигуры, ограниченной графиками линиями y[sub]1[/sub](x) и y[sub]2[/sub](x), вычисляется с помощью двойного интеграла
где y[sub]1[/sub](x) = y[sub]2[/sub](x) при x = x[sub]1[/sub], x = x[sub]2[/sub] и y[sub]1[/sub](x) < y[sub]2[/sub](x) при x[sub]1[/sub] < x < x[sub]2[/sub]. Если уравнения линий можно записать в виде x = x[sub]1[/sub](y) и x = x[sub]2[/sub](y), то интеграл примет вид
где x[sub]1[/sub](y) = x[sub]2[/sub](y) при y = y[sub]1[/sub], y = y[sub]2[/sub] и x[sub]1[/sub](y) < x[sub]2[/sub](y) при y[sub]1[/sub] < y < y[sub]2[/sub].
В данном случае проще использовать второй вариант: x[sub]1[/sub] = 2y, x[sub]2[/sub] = 8y, приравнивая x[sub]1[/sub] = x[sub]2[/sub], получаем
причём при 0 < y < 9 имеем x[sub]1[/sub] < x[sub]2[/sub].
Тогда искомая площадь будет равна
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