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Консультация № 197068
13.11.2019, 18:36
0.00 руб.
15.11.2019, 15:41
0
3
1
Здравствуйте!
Найти с помощью двойного интеграла площадь S
области D, ограниченной графиками функций
y = x2 + 4x + 3
y = 4x + 732
Сделать чертеж
Найти с помощью двойного интеграла площадь S
области D, ограниченной графиками функций
y = x2 + 4x + 3
y = 4x + 732
Сделать чертеж
Обсуждение
19.11.2019, 13:51
общий
Адресаты:
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, 11:21
общий
это ответ
Здравствуйте, mustang289!
Площадь области D, ограниченной графиками функций y[sub]1[/sub](x) и y[sub]2[/sub](x), вычисляется с помощью двойного интеграла
который в свою очередь сводится к повторному
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].
В данном случае y[sub]1[/sub] = x[sup]2[/sup]+4x+3, y[sub]2[/sub] = 4x+732, приравнивая y[sub]1[/sub] = y[sub]2[/sub], получаем
причём при -27 < x < 27 имеем y[sub]1[/sub] < y[sub]2[/sub].
Тогда искомая площадь будет равна
Площадь области D, ограниченной графиками функций y[sub]1[/sub](x) и y[sub]2[/sub](x), вычисляется с помощью двойного интеграла
который в свою очередь сводится к повторному
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].
В данном случае y[sub]1[/sub] = x[sup]2[/sup]+4x+3, y[sub]2[/sub] = 4x+732, приравнивая y[sub]1[/sub] = y[sub]2[/sub], получаем
причём при -27 < x < 27 имеем y[sub]1[/sub] < y[sub]2[/sub].
Тогда искомая площадь будет равна
24.11.2019, 02:47
общий
Адресаты:
У Вас пределы интегрирования внешнего интеграла по dx постоянны от -27 до +27, хотя ширина зоны мысленно заштрихованной площади сужается при уменьшении ординаты от 840 до 0 .
Мне кажется, Вы захватили бОльшую площадь, как будто она ограничена вертикальными стенками от x=-27 до x=+27 .
Грубый прикид сравнения искомой площади можно сопоставить с квадратом [$916$]x=30 * [$916$]y=400 площадью 30*400 = 12 000, вдвое мЕньшей чем в Ответе.
Или я чего-то не понимаю?
Мне кажется, Вы захватили бОльшую площадь, как будто она ограничена вертикальными стенками от x=-27 до x=+27 .
Грубый прикид сравнения искомой площади можно сопоставить с квадратом [$916$]x=30 * [$916$]y=400 площадью 30*400 = 12 000, вдвое мЕньшей чем в Ответе.
Или я чего-то не понимаю?
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