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Консультация № 198484
07.05.2020, 21:59
0.00 руб.
12.05.2020, 17:34
0
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Как установить расходимость следующего интеграла:
Как установить расходимость следующего интеграла:
Обсуждение
14.05.2020, 20:02
общий
это ответ
Здравствуйте, xxgggi!
Подинтегральная функция непрерывна на всём отрезке интегрирования [-2, 2], за исключением точек x = [$177$]1. Поэтому интеграл следует разбить на сумму трёх интегралов:
каждый из которых является несобственным интегралом второго рода (с подинтегральной функцией, стремящейся к бесконечности на границе отрезка интегрирования). Так как
то соответствующие интегралы расходятся. Следовательно, расходится и исходный интеграл.
Подинтегральная функция непрерывна на всём отрезке интегрирования [-2, 2], за исключением точек x = [$177$]1. Поэтому интеграл следует разбить на сумму трёх интегралов:
каждый из которых является несобственным интегралом второго рода (с подинтегральной функцией, стремящейся к бесконечности на границе отрезка интегрирования). Так как
то соответствующие интегралы расходятся. Следовательно, расходится и исходный интеграл.
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