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Консультация № 185675
26.03.2012, 14:45
76.63 руб.
0
4
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Найти массу тела заданного неравенствами и имеющего заданную плотность µ, сделать чертеж.
распишите ответ на бумаге / в редакторе формул если Вас не затруднит. Заранее спасибо :)
Найти массу тела заданного неравенствами и имеющего заданную плотность µ, сделать чертеж.
распишите ответ на бумаге / в редакторе формул если Вас не затруднит. Заранее спасибо :)
Обсуждение
26.03.2012, 16:06
общий
это ответ
Здравствуйте, Stanislav Bolshakov!
Область интегрирования представляет собой четвертинку верхней части шара.
Перейдём к цилиндрическим координатам:
Якобиан равен
.
В таких координатах пределы интегрирования понятны: z меняется от 3 до 5,
от 0 до 
а r:
.
Так что искомый интеграл в новых координатах
Область интегрирования представляет собой четвертинку верхней части шара.
Перейдём к цилиндрическим координатам:
Якобиан равен
.В таких координатах пределы интегрирования понятны: z меняется от 3 до 5,
от 0 до а r:.Так что искомый интеграл в новых координатах
26.03.2012, 17:04
общий
26.03.2012, 17:04
А нём точно есть необходимость? Я, если честно, думаю, что не смогу нарисовать понятней, чем объяснить :)
1. Представьте шар радиусом 5 с центром в начале координат.
2. Плоскость z=3 делит его на две части: верхнюю и нижнюю. Нам нужна верхняя, нижнюю отрезали.
3. Оставшийся холмик делится плоскостями x=0 и y=0 на 4 куска. Нам нужен тот, который соответствует области с положительными x и y.
Это и есть искомая область интегрирования. На каком шаге возникает затруднение?
1. Представьте шар радиусом 5 с центром в начале координат.
2. Плоскость z=3 делит его на две части: верхнюю и нижнюю. Нам нужна верхняя, нижнюю отрезали.
3. Оставшийся холмик делится плоскостями x=0 и y=0 на 4 куска. Нам нужен тот, который соответствует области с положительными x и y.
Это и есть искомая область интегрирования. На каком шаге возникает затруднение?
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