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Консультация № 87799
20.05.2007, 20:40
0.00 руб.
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1
здрасте!=)))Помигите пожалуйста мне решить несколько примеров(интегралов) по математическому анализу.
1)Найти площадь ограниченную графиками:
x=(y-2)^3, x=4y-8
2)Найти площадь ограниченную графиками:
Дана система|x=3cos(t)
|y=8sin(t), y>=4
3)Найти длину кривой:
p=cos(2t)
4)Найти площадь ограниченную графиками:
y=arccos(x^1/2)-(x-x^2)^1/2+4, 0<=x<=1/2
5)Найти площадь ограниченную графиками:
Дана система|x=4cos^3(t)
|y=4sin^3(t), пи/6<=t<=пи/4
6)Найти длину кривой:
p=8(1-cos(t)), -2пи/3<=t<=0
всё это нужно решить с помощью интегралов, заранее спасибо=)
1)Найти площадь ограниченную графиками:
x=(y-2)^3, x=4y-8
2)Найти площадь ограниченную графиками:
Дана система|x=3cos(t)
|y=8sin(t), y>=4
3)Найти длину кривой:
p=cos(2t)
4)Найти площадь ограниченную графиками:
y=arccos(x^1/2)-(x-x^2)^1/2+4, 0<=x<=1/2
5)Найти площадь ограниченную графиками:
Дана система|x=4cos^3(t)
|y=4sin^3(t), пи/6<=t<=пи/4
6)Найти длину кривой:
p=8(1-cos(t)), -2пи/3<=t<=0
всё это нужно решить с помощью интегралов, заранее спасибо=)
Обсуждение
Неизвестный
22.05.2007, 17:49
общий
это ответ
Здравствуйте, Костенко Дмитрий Александрович!
1
Для удобства поставим в сообтветсвие х=У у=Х
Приравниваем правые части равенств
либо решаем кубическрое уравнение(корень 2 очевиден а потом оно превращается в квадратное)
либо схематичным графиком корни 0 и 2
Тогда считаем
(интеграл (от 0 до 2 ))((Х-2)^3-4X+8)dX
чтоб его посчитать нужно раскрыть все скобки и преобразовать согласно тождества
интеграл суммы равен сумме интгралов
там получатся табличные
не привожу злдесь
так ккк нет смысла парится без мафтайп для таких интегралов
2 остальное принципиально не знаю
открой секрет где такие дают??
надеюсь не в школе а то я себя дауном считать буду
1
Для удобства поставим в сообтветсвие х=У у=Х
Приравниваем правые части равенств
либо решаем кубическрое уравнение(корень 2 очевиден а потом оно превращается в квадратное)
либо схематичным графиком корни 0 и 2
Тогда считаем
(интеграл (от 0 до 2 ))((Х-2)^3-4X+8)dX
чтоб его посчитать нужно раскрыть все скобки и преобразовать согласно тождества
интеграл суммы равен сумме интгралов
там получатся табличные
не привожу злдесь
так ккк нет смысла парится без мафтайп для таких интегралов
2 остальное принципиально не знаю
открой секрет где такие дают??
надеюсь не в школе а то я себя дауном считать буду
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