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Консультация № 185776
08.04.2012, 12:03
100.00 руб.
0
4
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
а) найти несобственный интеграл (xdx)/(x^2-3)^3/2 (в числителе - икс умножить на дэ икс, в знаменателе - икс в квадрате минус три, всё это в степени три вторых). Предел интегрирования - от плюс бесконечности до минус двух.
б) вычислить несобственный интеграл или установить его расходимость:
dx/sqrt((x+1)^3) (дэ икс, деленное на квадратный корень из икс плюс один в кубе). Предел интегрирования - от нуля до минус единицы.
а) найти несобственный интеграл (xdx)/(x^2-3)^3/2 (в числителе - икс умножить на дэ икс, в знаменателе - икс в квадрате минус три, всё это в степени три вторых). Предел интегрирования - от плюс бесконечности до минус двух.
б) вычислить несобственный интеграл или установить его расходимость:
dx/sqrt((x+1)^3) (дэ икс, деленное на квадратный корень из икс плюс один в кубе). Предел интегрирования - от нуля до минус единицы.
Обсуждение
08.04.2012, 12:57
общий
это ответ
Здравствуйте, Aleksandrkib!
а)
.
Первый интеграл равен нулю как интеграл от нечётной функции, если сходится(а он сходится).
Делаем замену
,
.
б)
.
Значит расходится.
а)
.Первый интеграл равен нулю как интеграл от нечётной функции, если сходится(а он сходится).
Делаем замену
,.б)
.Значит расходится.
10.04.2012, 06:50
общий
10.04.2012, 07:08
Здравствуйте, vanger! Прошу прощения, но я неправильно указал пределы интегрирования. В первом случае верхний предел - плюс бесконечность, нижний - минус два, во втором верхний предел - 0, нижний - минус один (т.е. всё наоборот). Не могли бы Вы перерешать данные интегралы?
За свою оплошность я увеличил стоимость вопроса.
За свою оплошность я увеличил стоимость вопроса.
10.04.2012, 14:36
общий
Адресаты:
Добрый день! Т.е. просто все пределы интегрирования местами поменялись? На ход решения это не влияет - от этого только знак интегралов поменяется. Впрочем, изменения в ответ сейчас внесу.
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