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Консультация № 163763
31.03.2009, 09:52
0.00 руб.
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Здравствуйте, помогите пожалуйста решить задачи:
1. Вычислить несобственный интеграл или установить его расходимость инт от п/2 до 0 ctgx dx
2. Вычислить приближенно определенный интеграл, используя разложение подынтегральной функции в степенной ряд и почленное интегрирование полученного ряда. Результат должен быть получен с точностью до 0,001. инт от 0,1 до 0 dx/корень кубический(8+х в кубе)
1. Вычислить несобственный интеграл или установить его расходимость инт от п/2 до 0 ctgx dx
2. Вычислить приближенно определенный интеграл, используя разложение подынтегральной функции в степенной ряд и почленное интегрирование полученного ряда. Результат должен быть получен с точностью до 0,001. инт от 0,1 до 0 dx/корень кубический(8+х в кубе)
Обсуждение
06.04.2009, 10:55
общий
1. Интеграл расходящийся, т.к. в результате интегрирования получим ln(sin(0)), т.е. бесконечность
2. Раскладываем саму функцию.
(1+z)^alfa = 1 + Sum[n=1, infinity] alfa*(alfa-1)*...*(alfa-n+1)*z^n/(n!)
Если теперь вспомнить, что z=x/2, alfa=-1/3, то легко осуществить почленное интегрирование такого ряда и вычислить его с необходимой точностью.
2. Раскладываем саму функцию.
(1+z)^alfa = 1 + Sum[n=1, infinity] alfa*(alfa-1)*...*(alfa-n+1)*z^n/(n!)
Если теперь вспомнить, что z=x/2, alfa=-1/3, то легко осуществить почленное интегрирование такого ряда и вычислить его с необходимой точностью.
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