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Консультация № 187878
07.06.2014, 17:18
78.80 руб.
0
1
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Вычислить несобственный интеграл или доказать его расходимость:
Интеграл dx/(x-1)^2, нижний предел интегрирования 1, верхний предел интегрирования 2 (т.е. интеграл от 1 до 2 дэ икс, делённое на икс минус один в квадрате).
Вычислить несобственный интеграл или доказать его расходимость:
Интеграл dx/(x-1)^2, нижний предел интегрирования 1, верхний предел интегрирования 2 (т.е. интеграл от 1 до 2 дэ икс, делённое на икс минус один в квадрате).
Обсуждение
07.06.2014, 17:39
общий
это ответ
Здравствуйте, Aleksandrkib!
12[$8747$]dx/(x-1)2=12[$8747$](x-1)-2d(x-1)=-(x-1)-1|12=-1/(2-1)+1/(1-1)=-1+[$8734$]=[$8734$]
интеграл расходится
Также можно отметить, что если 01[$8747$]dx/x расходится, то очевидно, что интеграл вида 01[$8747$]dx/x2 (равный рассматриваемому, что доказывается подстановкой t=x-1), значения подынтегральной функции которого в этом диапазоне не меньше, чем у 1/x, такде должен расходиться.
12[$8747$]dx/(x-1)2=12[$8747$](x-1)-2d(x-1)=-(x-1)-1|12=-1/(2-1)+1/(1-1)=-1+[$8734$]=[$8734$]
интеграл расходится
Также можно отметить, что если 01[$8747$]dx/x расходится, то очевидно, что интеграл вида 01[$8747$]dx/x2 (равный рассматриваемому, что доказывается подстановкой t=x-1), значения подынтегральной функции которого в этом диапазоне не меньше, чем у 1/x, такде должен расходиться.
5
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