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Консультация № 203137
05.09.2022, 14:44
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Построить область интегрирования, изменить порядок интегрирования в интеграле.
Номер варианта 6
Построить область интегрирования, изменить порядок интегрирования в интеграле.
Номер варианта 6
Прикрепленные файлы:
Обсуждение
07.09.2022, 00:34
общий
это ответ
Здравствуйте, Anna!
Пусть дан двукратный, или повторный, интеграл
Из указанных пределов интегрирования следует, что область интегрирования задана неравенствами 
Посмотрите на график в первом прикреплённом файле. Из него видно, что при заданном промежутке значений
функция 
не определена. Поэтому заданный интеграл невозможно вычислить.
Ситуация изменится, если дан двукратный интеграл
Из указанных пределов интегрирования следует, что область интегрирования задана неравенствами 
Соответствующая область интегрирования обозначена на рисунке во втором прикреплённом файле заливкой серым цветом. В этом случае представленную область можно разбить на две части:
1) часть, которая расположена ниже оси абсцисс. Она определяется неравенствами
2) часть, которая расположена выше оси абсцисс. Она определяется неравенствами
Поэтому заданный порядок интегрирования нужно изменить следующим образом:
Пусть дан двукратный, или повторный, интеграл
Из указанных пределов интегрирования следует, что область интегрирования задана неравенствами Посмотрите на график в первом прикреплённом файле. Из него видно, что при заданном промежутке значений
функция не определена. Поэтому заданный интеграл невозможно вычислить.Ситуация изменится, если дан двукратный интеграл
Из указанных пределов интегрирования следует, что область интегрирования задана неравенствами Соответствующая область интегрирования обозначена на рисунке во втором прикреплённом файле заливкой серым цветом. В этом случае представленную область можно разбить на две части:1) часть, которая расположена ниже оси абсцисс. Она определяется неравенствами
2) часть, которая расположена выше оси абсцисс. Она определяется неравенствами
Поэтому заданный порядок интегрирования нужно изменить следующим образом:
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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